%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP038+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:42:42 AM UTC 2025
% Result : Theorem 4.93s 5.15s
% Output : Proof 5.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : TOP038+1 : TPTP v9.0.0. Released v3.4.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 14:00:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.93/5.15 % SZS status Theorem
% 4.93/5.15 % SZS output start Proof
% 4.93/5.15 tff(k4_subset_1_type, type, (
% 4.93/5.15 k4_subset_1: ( $i * $i * $i ) > $i)).
% 4.93/5.15 tff(k4_pre_topc_type, type, (
% 4.93/5.15 k4_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 4.93/5.15 tff(tptp_fun_D_3_type, type, (
% 4.93/5.15 tptp_fun_D_3: $i)).
% 4.93/5.15 tff(k4_tsp_2_type, type, (
% 4.93/5.15 k4_tsp_2: ( $i * $i ) > $i)).
% 4.93/5.15 tff(tptp_fun_B_1_type, type, (
% 4.93/5.15 tptp_fun_B_1: $i)).
% 4.93/5.15 tff(tptp_fun_A_0_type, type, (
% 4.93/5.15 tptp_fun_A_0: $i)).
% 4.93/5.15 tff(tptp_fun_C_2_type, type, (
% 4.93/5.15 tptp_fun_C_2: $i)).
% 4.93/5.15 tff(u1_struct_0_type, type, (
% 4.93/5.15 u1_struct_0: $i > $i)).
% 4.93/5.15 tff(k2_xboole_0_type, type, (
% 4.93/5.15 k2_xboole_0: ( $i * $i ) > $i)).
% 4.93/5.15 tff(m1_subset_1_type, type, (
% 4.93/5.15 m1_subset_1: ( $i * $i ) > $o)).
% 4.93/5.15 tff(k1_zfmisc_1_type, type, (
% 4.93/5.15 k1_zfmisc_1: $i > $i)).
% 4.93/5.15 tff(l1_struct_0_type, type, (
% 4.93/5.15 l1_struct_0: $i > $o)).
% 4.93/5.15 tff(l1_pre_topc_type, type, (
% 4.93/5.15 l1_pre_topc: $i > $o)).
% 4.93/5.15 tff(m2_tsp_1_type, type, (
% 4.93/5.15 m2_tsp_1: ( $i * $i ) > $o)).
% 4.93/5.15 tff(v2_tsp_2_type, type, (
% 4.93/5.15 v2_tsp_2: ( $i * $i ) > $o)).
% 4.93/5.15 tff(v3_struct_0_type, type, (
% 4.93/5.15 v3_struct_0: $i > $o)).
% 4.93/5.15 tff(v2_pre_topc_type, type, (
% 4.93/5.15 v2_pre_topc: $i > $o)).
% 4.93/5.15 tff(v1_funct_2_type, type, (
% 4.93/5.15 v1_funct_2: ( $i * $i * $i ) > $o)).
% 4.93/5.15 tff(m2_relset_1_type, type, (
% 4.93/5.15 m2_relset_1: ( $i * $i * $i ) > $o)).
% 4.93/5.15 tff(v5_pre_topc_type, type, (
% 4.93/5.15 v5_pre_topc: ( $i * $i * $i ) > $o)).
% 4.93/5.15 tff(v1_funct_1_type, type, (
% 4.93/5.15 v1_funct_1: $i > $o)).
% 4.93/5.15 tff(m1_pre_topc_type, type, (
% 4.93/5.15 m1_pre_topc: ( $i * $i ) > $o)).
% 4.93/5.15 tff(m1_relset_1_type, type, (
% 4.93/5.15 m1_relset_1: ( $i * $i * $i ) > $o)).
% 4.93/5.15 tff(k1_tsp_2_type, type, (
% 4.93/5.15 k1_tsp_2: ( $i * $i ) > $i)).
% 4.93/5.15 tff(k3_xboole_0_type, type, (
% 4.93/5.15 k3_xboole_0: ( $i * $i ) > $i)).
% 4.93/5.15 tff(k3_tex_4_type, type, (
% 4.93/5.15 k3_tex_4: ( $i * $i ) > $i)).
% 4.93/5.15 tff(tptp_fun_B_15_type, type, (
% 4.93/5.15 tptp_fun_B_15: $i > $i)).
% 4.93/5.15 tff(k5_subset_1_type, type, (
% 4.93/5.15 k5_subset_1: ( $i * $i * $i ) > $i)).
% 4.93/5.15 tff(k1_xboole_0_type, type, (
% 4.93/5.15 k1_xboole_0: $i)).
% 4.93/5.15 tff(v1_xboole_0_type, type, (
% 4.93/5.15 v1_xboole_0: $i > $o)).
% 4.93/5.15 tff(tptp_fun_B_21_type, type, (
% 4.93/5.15 tptp_fun_B_21: $i > $i)).
% 4.93/5.15 tff(v3_tops_1_type, type, (
% 4.93/5.15 v3_tops_1: ( $i * $i ) > $o)).
% 4.93/5.15 tff(v2_tops_1_type, type, (
% 4.93/5.15 v2_tops_1: ( $i * $i ) > $o)).
% 4.93/5.15 tff(v5_membered_type, type, (
% 4.93/5.15 v5_membered: $i > $o)).
% 4.93/5.15 tff(v4_membered_type, type, (
% 4.93/5.15 v4_membered: $i > $o)).
% 4.93/5.15 tff(v3_membered_type, type, (
% 4.93/5.15 v3_membered: $i > $o)).
% 4.93/5.15 tff(v2_membered_type, type, (
% 4.93/5.15 v2_membered: $i > $o)).
% 4.93/5.15 tff(v1_membered_type, type, (
% 4.93/5.15 v1_membered: $i > $o)).
% 4.93/5.15 tff(v4_pre_topc_type, type, (
% 4.93/5.15 v4_pre_topc: ( $i * $i ) > $o)).
% 4.93/5.15 tff(v3_pre_topc_type, type, (
% 4.93/5.15 v3_pre_topc: ( $i * $i ) > $o)).
% 4.93/5.15 tff(tptp_fun_E_4_type, type, (
% 4.93/5.15 tptp_fun_E_4: ( $i * $i * $i ) > $i)).
% 4.93/5.15 tff(1,plain,
% 4.93/5.15 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(2,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[1])).
% 4.93/5.15 tff(3,plain,
% 4.93/5.15 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(4,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[3])).
% 4.93/5.15 tff(5,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.93/5.15 inference(transitivity,[status(thm)],[4, 2])).
% 4.93/5.15 tff(6,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(7,plain,
% 4.93/5.15 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((m2_tsp_1(B, A) => l1_pre_topc(B)) <=> (l1_pre_topc(B) | (~m2_tsp_1(B, A))))), (![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B)) <=> ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))), ((l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B))) <=> (l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))))), rewrite((l1_pre_topc(A) => ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A)))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))), ((l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(8,plain,
% 4.93/5.15 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[7])).
% 4.93/5.15 tff(9,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) => l1_pre_topc(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_tsp_1')).
% 4.93/5.15 tff(10,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[9, 8])).
% 4.93/5.15 tff(11,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[10, 6])).
% 4.93/5.15 tff(12,plain,(
% 4.93/5.15 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.93/5.15 inference(skolemize,[status(sab)],[11])).
% 4.93/5.15 tff(13,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[12, 5])).
% 4.93/5.15 tff(14,plain,
% 4.93/5.15 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))))))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(15,plain,
% 4.93/5.15 ((((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))))))) <=> ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))))))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(16,plain,
% 4.93/5.15 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)))))))) <=> (((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & ((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)))))))),
% 4.93/5.15 inference(monotonicity,[status(thm)],[15])).
% 4.93/5.15 tff(17,plain,
% 4.93/5.15 ((((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)) & (((~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0)) & (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)))))))) <=> ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))))))),
% 4.93/5.15 inference(transitivity,[status(thm)],[16, 14])).
% 4.93/5.15 tff(18,plain,
% 4.93/5.15 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (k4_pre_topc(A, B, k4_tsp_2(A, B), k4_subset_1(u1_struct_0(A), C, D)) = k4_subset_1(u1_struct_0(B), k4_pre_topc(A, B, k4_tsp_2(A, B), C), k4_pre_topc(A, B, k4_tsp_2(A, B), D)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (k4_pre_topc(A, B, k4_tsp_2(A, B), k4_subset_1(u1_struct_0(A), C, D)) = k4_subset_1(u1_struct_0(B), k4_pre_topc(A, B, k4_tsp_2(A, B), C), k4_pre_topc(A, B, k4_tsp_2(A, B), D))))))))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(19,plain,
% 4.93/5.15 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (k4_pre_topc(A, B, k4_tsp_2(A, B), k4_subset_1(u1_struct_0(A), C, D)) = k4_subset_1(u1_struct_0(B), k4_pre_topc(A, B, k4_tsp_2(A, B), C), k4_pre_topc(A, B, k4_tsp_2(A, B), D)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (k4_pre_topc(A, B, k4_tsp_2(A, B), k4_subset_1(u1_struct_0(A), C, D)) = k4_subset_1(u1_struct_0(B), k4_pre_topc(A, B, k4_tsp_2(A, B), C), k4_pre_topc(A, B, k4_tsp_2(A, B), D))))))))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(20,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => (k4_pre_topc(A, B, k4_tsp_2(A, B), k4_subset_1(u1_struct_0(A), C, D)) = k4_subset_1(u1_struct_0(B), k4_pre_topc(A, B, k4_tsp_2(A, B), C), k4_pre_topc(A, B, k4_tsp_2(A, B), D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t31_tsp_2')).
% 4.93/5.15 tff(21,plain,
% 4.93/5.15 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (k4_pre_topc(A, B, k4_tsp_2(A, B), k4_subset_1(u1_struct_0(A), C, D)) = k4_subset_1(u1_struct_0(B), k4_pre_topc(A, B, k4_tsp_2(A, B), C), k4_pre_topc(A, B, k4_tsp_2(A, B), D)))))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[20, 19])).
% 4.93/5.15 tff(22,plain,
% 4.93/5.15 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (k4_pre_topc(A, B, k4_tsp_2(A, B), k4_subset_1(u1_struct_0(A), C, D)) = k4_subset_1(u1_struct_0(B), k4_pre_topc(A, B, k4_tsp_2(A, B), C), k4_pre_topc(A, B, k4_tsp_2(A, B), D)))))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[21, 18])).
% 4.93/5.15 tff(23,plain,
% 4.93/5.15 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (k4_pre_topc(A, B, k4_tsp_2(A, B), k4_subset_1(u1_struct_0(A), C, D)) = k4_subset_1(u1_struct_0(B), k4_pre_topc(A, B, k4_tsp_2(A, B), C), k4_pre_topc(A, B, k4_tsp_2(A, B), D)))))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[22, 18])).
% 4.93/5.15 tff(24,plain,
% 4.93/5.15 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) | (k4_pre_topc(A, B, k4_tsp_2(A, B), k4_subset_1(u1_struct_0(A), C, D)) = k4_subset_1(u1_struct_0(B), k4_pre_topc(A, B, k4_tsp_2(A, B), C), k4_pre_topc(A, B, k4_tsp_2(A, B), D)))))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[23, 18])).
% 4.93/5.15 tff(25,plain,
% 4.93/5.15 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0) & (~v3_struct_0(B!1)) & v2_tsp_2(B!1, A!0) & m2_tsp_1(B!1, A!0) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[24, 17])).
% 4.93/5.15 tff(26,plain,
% 4.93/5.15 (l1_pre_topc(A!0)),
% 4.93/5.15 inference(and_elim,[status(thm)],[25])).
% 4.93/5.15 tff(27,plain,
% 4.93/5.15 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | (~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0))))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(28,plain,
% 4.93/5.15 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0))))),
% 4.93/5.15 inference(quant_inst,[status(thm)],[])).
% 4.93/5.15 tff(29,plain,
% 4.93/5.15 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A))))) | (~l1_pre_topc(A!0)) | ![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[28, 27])).
% 4.93/5.15 tff(30,plain,
% 4.93/5.15 (![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))),
% 4.93/5.15 inference(unit_resolution,[status(thm)],[29, 26, 13])).
% 4.93/5.15 tff(31,plain,
% 4.93/5.15 (m2_tsp_1(B!1, A!0)),
% 4.93/5.15 inference(and_elim,[status(thm)],[25])).
% 4.93/5.15 tff(32,plain,
% 4.93/5.15 (((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))) <=> ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(33,plain,
% 4.93/5.15 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | (l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0)))),
% 4.93/5.15 inference(quant_inst,[status(thm)],[])).
% 4.93/5.15 tff(34,plain,
% 4.93/5.15 ((~![B: $i] : (l1_pre_topc(B) | (~m2_tsp_1(B, A!0)))) | l1_pre_topc(B!1) | (~m2_tsp_1(B!1, A!0))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[33, 32])).
% 4.93/5.15 tff(35,plain,
% 4.93/5.15 (l1_pre_topc(B!1)),
% 4.93/5.15 inference(unit_resolution,[status(thm)],[34, 31, 30])).
% 4.93/5.15 tff(36,plain,
% 4.93/5.15 (^[A: $i] : refl((l1_struct_0(A) | (~l1_pre_topc(A))) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(37,plain,
% 4.93/5.15 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[36])).
% 4.93/5.15 tff(38,plain,
% 4.93/5.15 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(39,plain,
% 4.93/5.15 (^[A: $i] : rewrite((l1_pre_topc(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_pre_topc(A))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(40,plain,
% 4.93/5.15 (![A: $i] : (l1_pre_topc(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[39])).
% 4.93/5.15 tff(41,axiom,(![A: $i] : (l1_pre_topc(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 4.93/5.15 tff(42,plain,
% 4.93/5.15 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[41, 40])).
% 4.93/5.15 tff(43,plain,
% 4.93/5.15 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[42, 38])).
% 4.93/5.15 tff(44,plain,(
% 4.93/5.15 ![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.93/5.15 inference(skolemize,[status(sab)],[43])).
% 4.93/5.15 tff(45,plain,
% 4.93/5.15 (![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[44, 37])).
% 4.93/5.15 tff(46,plain,
% 4.93/5.15 (((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(47,plain,
% 4.93/5.15 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(B!1) | (~l1_pre_topc(B!1)))),
% 4.93/5.15 inference(quant_inst,[status(thm)],[])).
% 4.93/5.15 tff(48,plain,
% 4.93/5.15 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(B!1) | (~l1_pre_topc(B!1))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[47, 46])).
% 4.93/5.15 tff(49,plain,
% 4.93/5.15 (l1_struct_0(B!1)),
% 4.93/5.15 inference(unit_resolution,[status(thm)],[48, 45, 35])).
% 4.93/5.15 tff(50,plain,
% 4.93/5.15 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(51,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[50])).
% 4.93/5.15 tff(52,plain,
% 4.93/5.15 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(53,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[52])).
% 4.93/5.15 tff(54,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.93/5.15 inference(transitivity,[status(thm)],[53, 51])).
% 4.93/5.15 tff(55,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(56,plain,
% 4.93/5.15 (^[A: $i] : rewrite((l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(57,plain,
% 4.93/5.15 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[56])).
% 4.93/5.15 tff(58,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_tsp_1')).
% 4.93/5.15 tff(59,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[58, 57])).
% 4.93/5.15 tff(60,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[59, 55])).
% 4.93/5.15 tff(61,plain,(
% 4.93/5.15 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.93/5.15 inference(skolemize,[status(sab)],[60])).
% 4.93/5.15 tff(62,plain,
% 4.93/5.15 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[61, 54])).
% 4.93/5.15 tff(63,plain,
% 4.93/5.15 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | (~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(64,plain,
% 4.93/5.15 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | ((~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0)))),
% 4.93/5.15 inference(quant_inst,[status(thm)],[])).
% 4.93/5.15 tff(65,plain,
% 4.93/5.15 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : (m2_tsp_1(B, A) <=> m1_pre_topc(B, A)))) | (~l1_pre_topc(A!0)) | ![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[64, 63])).
% 4.93/5.15 tff(66,plain,
% 4.93/5.15 (![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))),
% 4.93/5.15 inference(unit_resolution,[status(thm)],[65, 26, 62])).
% 4.93/5.15 tff(67,plain,
% 4.93/5.15 ((~![B: $i] : (m2_tsp_1(B, A!0) <=> m1_pre_topc(B, A!0))) | (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))),
% 4.93/5.15 inference(quant_inst,[status(thm)],[])).
% 4.93/5.15 tff(68,plain,
% 4.93/5.15 (m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0)),
% 4.93/5.15 inference(unit_resolution,[status(thm)],[67, 66])).
% 4.93/5.15 tff(69,plain,
% 4.93/5.15 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | (~m2_tsp_1(B!1, A!0)) | m1_pre_topc(B!1, A!0)),
% 4.93/5.15 inference(tautology,[status(thm)],[])).
% 4.93/5.15 tff(70,plain,
% 4.93/5.15 ((~(m2_tsp_1(B!1, A!0) <=> m1_pre_topc(B!1, A!0))) | m1_pre_topc(B!1, A!0)),
% 4.93/5.15 inference(unit_resolution,[status(thm)],[69, 31])).
% 4.93/5.15 tff(71,plain,
% 4.93/5.15 (m1_pre_topc(B!1, A!0)),
% 4.93/5.15 inference(unit_resolution,[status(thm)],[70, 68])).
% 4.93/5.15 tff(72,plain,
% 4.93/5.15 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(73,plain,
% 4.93/5.15 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[72])).
% 4.93/5.15 tff(74,plain,
% 4.93/5.15 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), rewrite((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(75,plain,
% 4.93/5.15 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[74])).
% 4.93/5.15 tff(76,plain,
% 4.93/5.15 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(77,plain,
% 4.93/5.15 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)))), trans(monotonicity(rewrite(((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) <=> (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B))), ((((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.15 inference(bind,[status(th)],[])).
% 4.93/5.15 tff(78,plain,
% 4.93/5.15 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.15 inference(quant_intro,[status(thm)],[77])).
% 4.93/5.15 tff(79,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k4_tsp_2(A, B), A, B)) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_tsp_2')).
% 4.93/5.15 tff(80,plain,
% 4.93/5.15 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[79, 78])).
% 4.93/5.15 tff(81,plain,
% 4.93/5.15 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[80, 76])).
% 4.93/5.15 tff(82,plain,(
% 4.93/5.15 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k4_tsp_2(A, B)) & v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A, B), A, B) & m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.15 inference(skolemize,[status(sab)],[81])).
% 4.93/5.15 tff(83,plain,
% 4.93/5.15 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[82, 75])).
% 4.93/5.15 tff(84,plain,
% 4.93/5.15 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.15 inference(modus_ponens,[status(thm)],[83, 73])).
% 4.93/5.15 tff(85,plain,
% 4.93/5.15 (v2_tsp_2(B!1, A!0)),
% 4.93/5.15 inference(and_elim,[status(thm)],[25])).
% 4.93/5.15 tff(86,plain,
% 4.93/5.15 (~v3_struct_0(B!1)),
% 4.93/5.15 inference(and_elim,[status(thm)],[25])).
% 4.93/5.15 tff(87,plain,
% 4.93/5.15 (v2_pre_topc(A!0)),
% 4.93/5.15 inference(and_elim,[status(thm)],[25])).
% 4.93/5.15 tff(88,plain,
% 4.93/5.15 (~v3_struct_0(A!0)),
% 4.93/5.15 inference(and_elim,[status(thm)],[25])).
% 4.93/5.15 tff(89,plain,
% 4.93/5.15 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(90,plain,
% 4.93/5.15 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(91,plain,
% 4.93/5.15 ((~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.93/5.15 inference(rewrite,[status(thm)],[])).
% 4.93/5.15 tff(92,plain,
% 4.93/5.15 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.15 inference(monotonicity,[status(thm)],[91])).
% 4.93/5.15 tff(93,plain,
% 4.93/5.15 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.15 inference(transitivity,[status(thm)],[92, 90])).
% 4.93/5.15 tff(94,plain,
% 4.93/5.15 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 4.93/5.15 inference(monotonicity,[status(thm)],[93])).
% 4.93/5.16 tff(95,plain,
% 4.93/5.16 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.16 inference(transitivity,[status(thm)],[94, 89])).
% 4.93/5.16 tff(96,plain,
% 4.93/5.16 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.16 inference(quant_inst,[status(thm)],[])).
% 4.93/5.16 tff(97,plain,
% 4.93/5.16 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k4_tsp_2(A, B))) | (~v1_funct_2(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k4_tsp_2(A, B), A, B)) | (~m2_relset_1(k4_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[96, 95])).
% 4.93/5.16 tff(98,plain,
% 4.93/5.16 ((~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.93/5.16 inference(unit_resolution,[status(thm)],[97, 88, 87, 26, 86, 85, 84])).
% 4.93/5.16 tff(99,plain,
% 4.93/5.16 (~((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.93/5.16 inference(unit_resolution,[status(thm)],[98, 71])).
% 4.93/5.16 tff(100,plain,
% 4.93/5.16 (((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.93/5.16 inference(tautology,[status(thm)],[])).
% 4.93/5.16 tff(101,plain,
% 4.93/5.16 (v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.93/5.16 inference(unit_resolution,[status(thm)],[100, 99])).
% 4.93/5.16 tff(102,plain,
% 4.93/5.16 (((~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k4_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_1(k4_tsp_2(A!0, B!1))),
% 4.93/5.16 inference(tautology,[status(thm)],[])).
% 4.93/5.16 tff(103,plain,
% 4.93/5.16 (v1_funct_1(k4_tsp_2(A!0, B!1))),
% 4.93/5.16 inference(unit_resolution,[status(thm)],[102, 99])).
% 4.93/5.16 tff(104,plain,
% 4.93/5.16 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))),
% 4.93/5.16 inference(bind,[status(th)],[])).
% 4.93/5.16 tff(105,plain,
% 4.93/5.16 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 4.93/5.16 inference(quant_intro,[status(thm)],[104])).
% 4.93/5.16 tff(106,plain,
% 4.93/5.16 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))))),
% 4.93/5.16 inference(bind,[status(th)],[])).
% 4.93/5.16 tff(107,plain,
% 4.93/5.16 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 4.93/5.16 inference(quant_intro,[status(thm)],[106])).
% 4.93/5.16 tff(108,plain,
% 4.93/5.16 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 4.93/5.16 inference(rewrite,[status(thm)],[])).
% 4.93/5.16 tff(109,plain,
% 4.93/5.16 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (k4_tsp_2(A, B) = k1_tsp_2(A, B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))))),
% 4.93/5.16 inference(bind,[status(th)],[])).
% 4.93/5.16 tff(110,plain,
% 4.93/5.16 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k4_tsp_2(A, B) = k1_tsp_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 4.93/5.16 inference(quant_intro,[status(thm)],[109])).
% 4.93/5.16 tff(111,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (k4_tsp_2(A, B) = k1_tsp_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_tsp_2')).
% 4.93/5.16 tff(112,plain,
% 4.93/5.16 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[111, 110])).
% 4.93/5.16 tff(113,plain,
% 4.93/5.16 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[112, 108])).
% 4.93/5.16 tff(114,plain,(
% 4.93/5.16 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)))),
% 4.93/5.16 inference(skolemize,[status(sab)],[113])).
% 4.93/5.16 tff(115,plain,
% 4.93/5.16 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[114, 107])).
% 4.93/5.16 tff(116,plain,
% 4.93/5.16 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[115, 105])).
% 4.93/5.16 tff(117,plain,
% 4.93/5.16 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 4.93/5.16 inference(rewrite,[status(thm)],[])).
% 4.93/5.16 tff(118,plain,
% 4.93/5.16 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 4.93/5.16 inference(rewrite,[status(thm)],[])).
% 4.93/5.16 tff(119,plain,
% 4.93/5.16 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))))),
% 4.93/5.16 inference(monotonicity,[status(thm)],[118])).
% 4.93/5.16 tff(120,plain,
% 4.93/5.16 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)))),
% 4.93/5.16 inference(transitivity,[status(thm)],[119, 117])).
% 4.93/5.16 tff(121,plain,
% 4.93/5.16 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)))),
% 4.93/5.16 inference(quant_inst,[status(thm)],[])).
% 4.93/5.16 tff(122,plain,
% 4.93/5.16 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (k4_tsp_2(A, B) = k1_tsp_2(A, B)) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[121, 120])).
% 4.93/5.16 tff(123,plain,
% 4.93/5.16 ((k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)) | (~m1_pre_topc(B!1, A!0))),
% 4.93/5.16 inference(unit_resolution,[status(thm)],[122, 88, 87, 26, 86, 85, 116])).
% 4.93/5.16 tff(124,plain,
% 4.93/5.16 (k4_tsp_2(A!0, B!1) = k1_tsp_2(A!0, B!1)),
% 4.93/5.16 inference(unit_resolution,[status(thm)],[123, 71])).
% 4.93/5.16 tff(125,plain,
% 4.93/5.16 (k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)),
% 4.93/5.16 inference(symmetry,[status(thm)],[124])).
% 4.93/5.16 tff(126,plain,
% 4.93/5.16 (m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.93/5.16 inference(monotonicity,[status(thm)],[125])).
% 4.93/5.16 tff(127,plain,
% 4.93/5.16 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 4.93/5.16 inference(bind,[status(th)],[])).
% 4.93/5.16 tff(128,plain,
% 4.93/5.16 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.93/5.16 inference(quant_intro,[status(thm)],[127])).
% 4.93/5.16 tff(129,plain,
% 4.93/5.16 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.93/5.16 inference(rewrite,[status(thm)],[])).
% 4.93/5.16 tff(130,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 4.93/5.16 tff(131,plain,
% 4.93/5.16 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[130, 129])).
% 4.93/5.16 tff(132,plain,(
% 4.93/5.16 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.93/5.16 inference(skolemize,[status(sab)],[131])).
% 4.93/5.16 tff(133,plain,
% 4.93/5.16 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[132, 128])).
% 4.93/5.16 tff(134,plain,
% 4.93/5.16 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.93/5.16 inference(quant_inst,[status(thm)],[])).
% 4.93/5.16 tff(135,plain,
% 4.93/5.16 (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.93/5.16 inference(unit_resolution,[status(thm)],[134, 133])).
% 4.93/5.16 tff(136,plain,
% 4.93/5.16 (^[A: $i, B: $i] : refl((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))),
% 4.93/5.16 inference(bind,[status(th)],[])).
% 4.93/5.16 tff(137,plain,
% 4.93/5.16 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.16 inference(quant_intro,[status(thm)],[136])).
% 4.93/5.16 tff(138,plain,
% 4.93/5.16 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))))), rewrite((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A))) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))))),
% 4.93/5.16 inference(bind,[status(th)],[])).
% 4.93/5.16 tff(139,plain,
% 4.93/5.16 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.16 inference(quant_intro,[status(thm)],[138])).
% 4.93/5.16 tff(140,plain,
% 4.93/5.16 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.16 inference(rewrite,[status(thm)],[])).
% 4.93/5.16 tff(141,plain,
% 4.93/5.16 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A))), ((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))), (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)))), trans(monotonicity(rewrite(((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) <=> (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B))), ((((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A)) => (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), ((((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.16 inference(bind,[status(th)],[])).
% 4.93/5.16 tff(142,plain,
% 4.93/5.16 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.16 inference(quant_intro,[status(thm)],[141])).
% 4.93/5.16 tff(143,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) & (~v3_struct_0(B))) & v2_tsp_2(B, A)) & m1_pre_topc(B, A)) => (((v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(k1_tsp_2(A, B), A, B)) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_tsp_2')).
% 4.93/5.16 tff(144,plain,
% 4.93/5.16 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[143, 142])).
% 4.93/5.16 tff(145,plain,
% 4.93/5.16 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[144, 140])).
% 4.93/5.16 tff(146,plain,(
% 4.93/5.16 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & (~v3_struct_0(B)) & v2_tsp_2(B, A) & m1_pre_topc(B, A))) | (v1_funct_1(k1_tsp_2(A, B)) & v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A, B), A, B) & m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.16 inference(skolemize,[status(sab)],[145])).
% 4.93/5.16 tff(147,plain,
% 4.93/5.16 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[146, 139])).
% 4.93/5.16 tff(148,plain,
% 4.93/5.16 (![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.16 inference(modus_ponens,[status(thm)],[147, 137])).
% 4.93/5.16 tff(149,plain,
% 4.93/5.16 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.16 inference(rewrite,[status(thm)],[])).
% 4.93/5.16 tff(150,plain,
% 4.93/5.16 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.16 inference(rewrite,[status(thm)],[])).
% 4.93/5.16 tff(151,plain,
% 4.93/5.16 ((~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.93/5.16 inference(rewrite,[status(thm)],[])).
% 4.93/5.16 tff(152,plain,
% 4.93/5.16 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.16 inference(monotonicity,[status(thm)],[151])).
% 4.93/5.16 tff(153,plain,
% 4.93/5.16 ((v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.16 inference(transitivity,[status(thm)],[152, 150])).
% 4.93/5.16 tff(154,plain,
% 4.93/5.16 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 4.93/5.16 inference(monotonicity,[status(thm)],[153])).
% 4.93/5.16 tff(155,plain,
% 4.93/5.16 (((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.16 inference(transitivity,[status(thm)],[154, 149])).
% 4.93/5.16 tff(156,plain,
% 4.93/5.16 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | (v3_struct_0(B!1) | (~v2_tsp_2(B!1, A!0)) | v3_struct_0(A!0) | (~m1_pre_topc(B!1, A!0)) | (~v2_pre_topc(A!0)) | (~l1_pre_topc(A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.93/5.17 inference(quant_inst,[status(thm)],[])).
% 4.93/5.17 tff(157,plain,
% 4.93/5.17 ((~![A: $i, B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | v3_struct_0(A) | (~m1_pre_topc(B, A)) | (~v2_pre_topc(A)) | (~l1_pre_topc(A)) | (~((~v1_funct_1(k1_tsp_2(A, B))) | (~v1_funct_2(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(k1_tsp_2(A, B), A, B)) | (~m2_relset_1(k1_tsp_2(A, B), u1_struct_0(A), u1_struct_0(B))))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v2_tsp_2(B!1, A!0)) | (~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[156, 155])).
% 4.93/5.17 tff(158,plain,
% 4.93/5.17 ((~m1_pre_topc(B!1, A!0)) | (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[157, 88, 87, 26, 86, 85, 148])).
% 4.93/5.17 tff(159,plain,
% 4.93/5.17 (~((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[158, 71])).
% 4.93/5.17 tff(160,plain,
% 4.93/5.17 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.93/5.17 inference(tautology,[status(thm)],[])).
% 4.93/5.17 tff(161,plain,
% 4.93/5.17 (m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[160, 159])).
% 4.93/5.17 tff(162,plain,
% 4.93/5.17 ((~(m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.93/5.17 inference(tautology,[status(thm)],[])).
% 4.93/5.17 tff(163,plain,
% 4.93/5.17 ((~(m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[162, 161])).
% 4.93/5.17 tff(164,plain,
% 4.93/5.17 (m1_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[163, 135])).
% 4.93/5.17 tff(165,plain,
% 4.93/5.17 (m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[164, 126])).
% 4.93/5.17 tff(166,plain,
% 4.93/5.17 (((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 4.93/5.17 inference(rewrite,[status(thm)],[])).
% 4.93/5.17 tff(167,plain,
% 4.93/5.17 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | (l1_struct_0(A!0) | (~l1_pre_topc(A!0)))),
% 4.93/5.17 inference(quant_inst,[status(thm)],[])).
% 4.93/5.17 tff(168,plain,
% 4.93/5.17 ((~![A: $i] : (l1_struct_0(A) | (~l1_pre_topc(A)))) | l1_struct_0(A!0) | (~l1_pre_topc(A!0))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[167, 166])).
% 4.93/5.17 tff(169,plain,
% 4.93/5.17 (l1_struct_0(A!0)),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[168, 26, 45])).
% 4.93/5.17 tff(170,plain,
% 4.93/5.17 (^[A: $i, B: $i, C: $i, D: $i] : refl((m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))),
% 4.93/5.17 inference(bind,[status(th)],[])).
% 4.93/5.17 tff(171,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.17 inference(quant_intro,[status(thm)],[170])).
% 4.93/5.17 tff(172,plain,
% 4.93/5.17 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> (((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))))), rewrite((((~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 4.93/5.17 inference(bind,[status(th)],[])).
% 4.93/5.17 tff(173,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.17 inference(quant_intro,[status(thm)],[172])).
% 4.93/5.17 tff(174,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))),
% 4.93/5.17 inference(rewrite,[status(thm)],[])).
% 4.93/5.17 tff(175,plain,
% 4.93/5.17 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))))),
% 4.93/5.17 inference(bind,[status(th)],[])).
% 4.93/5.17 tff(176,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))),
% 4.93/5.17 inference(quant_intro,[status(thm)],[175])).
% 4.93/5.17 tff(177,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_pre_topc')).
% 4.93/5.17 tff(178,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[177, 176])).
% 4.93/5.17 tff(179,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[178, 174])).
% 4.93/5.17 tff(180,plain,(
% 4.93/5.17 ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))))),
% 4.93/5.17 inference(skolemize,[status(sab)],[179])).
% 4.93/5.17 tff(181,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[180, 173])).
% 4.93/5.17 tff(182,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[181, 171])).
% 4.93/5.17 tff(183,plain,
% 4.93/5.17 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.93/5.17 inference(rewrite,[status(thm)],[])).
% 4.93/5.17 tff(184,plain,
% 4.93/5.17 ((m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.93/5.17 inference(rewrite,[status(thm)],[])).
% 4.93/5.17 tff(185,plain,
% 4.93/5.17 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.93/5.17 inference(monotonicity,[status(thm)],[184])).
% 4.93/5.17 tff(186,plain,
% 4.93/5.17 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.93/5.17 inference(transitivity,[status(thm)],[185, 183])).
% 4.93/5.17 tff(187,plain,
% 4.93/5.17 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.93/5.17 inference(quant_inst,[status(thm)],[])).
% 4.93/5.17 tff(188,plain,
% 4.93/5.17 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[187, 186])).
% 4.93/5.17 tff(189,plain,
% 4.93/5.17 ((~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[188, 182, 169])).
% 4.93/5.17 tff(190,plain,
% 4.93/5.17 (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1)))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[189, 165, 103, 101, 49])).
% 4.93/5.17 tff(191,plain,
% 4.93/5.17 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.93/5.17 inference(rewrite,[status(thm)],[])).
% 4.93/5.17 tff(192,plain,
% 4.93/5.17 ((m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.93/5.17 inference(rewrite,[status(thm)],[])).
% 4.93/5.17 tff(193,plain,
% 4.93/5.17 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | ((~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.93/5.17 inference(monotonicity,[status(thm)],[192])).
% 4.93/5.17 tff(194,plain,
% 4.93/5.17 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.93/5.17 inference(transitivity,[status(thm)],[193, 191])).
% 4.93/5.17 tff(195,plain,
% 4.93/5.17 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.93/5.17 inference(quant_inst,[status(thm)],[])).
% 4.93/5.17 tff(196,plain,
% 4.93/5.17 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k4_pre_topc(A, B, C, D), k1_zfmisc_1(u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[195, 194])).
% 4.93/5.17 tff(197,plain,
% 4.93/5.17 ((~l1_struct_0(B!1)) | m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1))) | (~v1_funct_1(k4_tsp_2(A!0, B!1))) | (~v1_funct_2(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k4_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[196, 182, 169])).
% 4.93/5.17 tff(198,plain,
% 4.93/5.17 (m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[197, 165, 103, 101, 49])).
% 4.93/5.17 tff(199,plain,
% 4.93/5.17 (^[A: $i, B: $i, C: $i] : refl(((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 4.93/5.17 inference(bind,[status(th)],[])).
% 4.93/5.17 tff(200,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 4.93/5.17 inference(quant_intro,[status(thm)],[199])).
% 4.93/5.17 tff(201,plain,
% 4.93/5.17 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 4.93/5.17 inference(bind,[status(th)],[])).
% 4.93/5.17 tff(202,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 4.93/5.17 inference(quant_intro,[status(thm)],[201])).
% 4.93/5.17 tff(203,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 4.93/5.17 inference(rewrite,[status(thm)],[])).
% 4.93/5.17 tff(204,plain,
% 4.93/5.17 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))))),
% 4.93/5.17 inference(bind,[status(th)],[])).
% 4.93/5.17 tff(205,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 4.93/5.17 inference(quant_intro,[status(thm)],[204])).
% 4.93/5.17 tff(206,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_subset_1')).
% 4.93/5.17 tff(207,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[206, 205])).
% 4.93/5.17 tff(208,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[207, 203])).
% 4.93/5.17 tff(209,plain,(
% 4.93/5.17 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 4.93/5.17 inference(skolemize,[status(sab)],[208])).
% 4.93/5.17 tff(210,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[209, 202])).
% 4.93/5.17 tff(211,plain,
% 4.93/5.17 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[210, 200])).
% 4.93/5.17 tff(212,plain,
% 4.93/5.17 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)) = k2_xboole_0(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)) = k2_xboole_0(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1)))))),
% 4.93/5.17 inference(rewrite,[status(thm)],[])).
% 4.93/5.17 tff(213,plain,
% 4.93/5.17 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)) = k2_xboole_0(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1)))))),
% 4.93/5.17 inference(quant_inst,[status(thm)],[])).
% 4.93/5.17 tff(214,plain,
% 4.93/5.17 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)) = k2_xboole_0(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[213, 212])).
% 4.93/5.17 tff(215,plain,
% 4.93/5.17 ((k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)) = k2_xboole_0(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k1_zfmisc_1(u1_struct_0(B!1)))) | (~m1_subset_1(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3), k1_zfmisc_1(u1_struct_0(B!1))))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[214, 211])).
% 4.93/5.17 tff(216,plain,
% 4.93/5.17 (k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)) = k2_xboole_0(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[215, 198, 190])).
% 4.93/5.17 tff(217,plain,
% 4.93/5.17 (k2_xboole_0(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))),
% 4.93/5.17 inference(symmetry,[status(thm)],[216])).
% 4.93/5.17 tff(218,plain,
% 4.93/5.17 (^[A: $i] : refl((~((~m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_15(A))))) <=> (~((~m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_15(A))))))),
% 4.93/5.17 inference(bind,[status(th)],[])).
% 4.93/5.17 tff(219,plain,
% 4.93/5.17 (![A: $i] : (~((~m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_15(A))))) <=> ![A: $i] : (~((~m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_15(A)))))),
% 4.93/5.17 inference(quant_intro,[status(thm)],[218])).
% 4.93/5.17 tff(220,plain,
% 4.93/5.17 (^[A: $i] : rewrite((m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A)) & v1_xboole_0(tptp_fun_B_15(A))) <=> (~((~m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_15(A))))))),
% 4.93/5.17 inference(bind,[status(th)],[])).
% 4.93/5.17 tff(221,plain,
% 4.93/5.17 (![A: $i] : (m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A)) & v1_xboole_0(tptp_fun_B_15(A))) <=> ![A: $i] : (~((~m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_15(A)))))),
% 4.93/5.17 inference(quant_intro,[status(thm)],[220])).
% 4.93/5.17 tff(222,plain,
% 4.93/5.17 (![A: $i] : ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) <=> ![A: $i] : ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B))),
% 4.93/5.17 inference(rewrite,[status(thm)],[])).
% 4.93/5.17 tff(223,axiom,(![A: $i] : ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc2_subset_1')).
% 4.93/5.17 tff(224,plain,
% 4.93/5.17 (![A: $i] : ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[223, 222])).
% 4.93/5.17 tff(225,plain,(
% 4.93/5.17 ![A: $i] : (m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A)) & v1_xboole_0(tptp_fun_B_15(A)))),
% 4.93/5.17 inference(skolemize,[status(sab)],[224])).
% 4.93/5.17 tff(226,plain,
% 4.93/5.17 (![A: $i] : (~((~m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_15(A)))))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[225, 221])).
% 4.93/5.17 tff(227,plain,
% 4.93/5.17 (![A: $i] : (~((~m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_15(A)))))),
% 4.93/5.17 inference(modus_ponens,[status(thm)],[226, 219])).
% 4.93/5.17 tff(228,plain,
% 4.93/5.17 ((~![A: $i] : (~((~m1_subset_1(tptp_fun_B_15(A), k1_zfmisc_1(A))) | (~v1_xboole_0(tptp_fun_B_15(A)))))) | (~((~m1_subset_1(tptp_fun_B_15(u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0))))))),
% 4.93/5.17 inference(quant_inst,[status(thm)],[])).
% 4.93/5.17 tff(229,plain,
% 4.93/5.17 (~((~m1_subset_1(tptp_fun_B_15(u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[228, 227])).
% 4.93/5.17 tff(230,plain,
% 4.93/5.17 (((~m1_subset_1(tptp_fun_B_15(u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0))))) | m1_subset_1(tptp_fun_B_15(u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 4.93/5.17 inference(tautology,[status(thm)],[])).
% 4.93/5.17 tff(231,plain,
% 4.93/5.17 (m1_subset_1(tptp_fun_B_15(u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 4.93/5.17 inference(unit_resolution,[status(thm)],[230, 229])).
% 4.93/5.17 tff(232,plain,
% 4.93/5.17 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))))),
% 4.93/5.17 inference(bind,[status(th)],[])).
% 4.93/5.17 tff(233,plain,
% 4.93/5.17 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.17 inference(quant_intro,[status(thm)],[232])).
% 4.93/5.17 tff(234,plain,
% 4.93/5.17 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))))),
% 4.93/5.18 inference(bind,[status(th)],[])).
% 4.93/5.18 tff(235,plain,
% 4.93/5.18 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.18 inference(quant_intro,[status(thm)],[234])).
% 4.93/5.18 tff(236,plain,
% 4.93/5.18 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.18 inference(transitivity,[status(thm)],[235, 233])).
% 4.93/5.18 tff(237,plain,
% 4.93/5.18 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))))),
% 4.93/5.18 inference(bind,[status(th)],[])).
% 4.93/5.18 tff(238,plain,
% 4.93/5.18 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.18 inference(quant_intro,[status(thm)],[237])).
% 4.93/5.18 tff(239,plain,
% 4.93/5.18 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.18 inference(rewrite,[status(thm)],[])).
% 4.93/5.18 tff(240,plain,
% 4.93/5.18 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))))), rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))), ((((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))))),
% 4.93/5.18 inference(bind,[status(th)],[])).
% 4.93/5.18 tff(241,plain,
% 4.93/5.18 (![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.18 inference(quant_intro,[status(thm)],[240])).
% 4.93/5.18 tff(242,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t38_tex_4')).
% 4.93/5.18 tff(243,plain,
% 4.93/5.18 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.18 inference(modus_ponens,[status(thm)],[242, 241])).
% 4.93/5.18 tff(244,plain,
% 4.93/5.18 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.18 inference(modus_ponens,[status(thm)],[243, 239])).
% 4.93/5.18 tff(245,plain,(
% 4.93/5.18 ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.18 inference(skolemize,[status(sab)],[244])).
% 4.93/5.18 tff(246,plain,
% 4.93/5.18 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.18 inference(modus_ponens,[status(thm)],[245, 238])).
% 4.93/5.18 tff(247,plain,
% 4.93/5.18 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))),
% 4.93/5.18 inference(modus_ponens,[status(thm)],[246, 236])).
% 4.93/5.18 tff(248,plain,
% 4.93/5.18 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C))))))),
% 5.01/5.18 inference(rewrite,[status(thm)],[])).
% 5.01/5.18 tff(249,plain,
% 5.01/5.18 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C))))))),
% 5.01/5.18 inference(quant_inst,[status(thm)],[])).
% 5.01/5.18 tff(250,plain,
% 5.01/5.18 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (k3_tex_4(A, k4_subset_1(u1_struct_0(A), B, C)) = k4_subset_1(u1_struct_0(A), k3_tex_4(A, B), k3_tex_4(A, C))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[249, 248])).
% 5.01/5.18 tff(251,plain,
% 5.01/5.18 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))),
% 5.01/5.18 inference(unit_resolution,[status(thm)],[250, 88, 26, 247])).
% 5.01/5.18 tff(252,plain,
% 5.01/5.18 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | ((~m1_subset_1(tptp_fun_B_15(u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | (~m1_subset_1(tptp_fun_B_15(u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C)))))),
% 5.01/5.18 inference(rewrite,[status(thm)],[])).
% 5.01/5.18 tff(253,plain,
% 5.01/5.18 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | ((~m1_subset_1(tptp_fun_B_15(u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C)))))),
% 5.01/5.18 inference(quant_inst,[status(thm)],[])).
% 5.01/5.18 tff(254,plain,
% 5.01/5.18 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | (~m1_subset_1(tptp_fun_B_15(u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C))))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[253, 252])).
% 5.01/5.18 tff(255,plain,
% 5.01/5.18 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C))))),
% 5.01/5.18 inference(unit_resolution,[status(thm)],[254, 251, 231])).
% 5.01/5.18 tff(256,plain,
% 5.01/5.18 (~((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))))),
% 5.01/5.18 inference(and_elim,[status(thm)],[25])).
% 5.01/5.18 tff(257,plain,
% 5.01/5.18 (m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.01/5.18 inference(or_elim,[status(thm)],[256])).
% 5.01/5.18 tff(258,plain,
% 5.01/5.18 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))))),
% 5.01/5.18 inference(rewrite,[status(thm)],[])).
% 5.01/5.18 tff(259,plain,
% 5.01/5.18 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))))),
% 5.01/5.18 inference(quant_inst,[status(thm)],[])).
% 5.01/5.18 tff(260,plain,
% 5.01/5.18 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[259, 258])).
% 5.01/5.18 tff(261,plain,
% 5.01/5.18 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))),
% 5.01/5.18 inference(unit_resolution,[status(thm)],[260, 257, 255])).
% 5.01/5.18 tff(262,plain,
% 5.01/5.18 (^[A: $i] : refl(((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A))))) <=> ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A))))))),
% 5.01/5.18 inference(bind,[status(th)],[])).
% 5.01/5.18 tff(263,plain,
% 5.01/5.18 (![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A)))))),
% 5.01/5.18 inference(quant_intro,[status(thm)],[262])).
% 5.01/5.18 tff(264,plain,
% 5.01/5.18 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_pre_topc(A) & l1_pre_topc(A)) <=> (~((~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~(v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~((~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~((~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> ((~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~(v2_pre_topc(A) & l1_pre_topc(A))) <=> ((~l1_pre_topc(A)) | (~v2_pre_topc(A))))), rewrite((m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(tptp_fun_B_21(A)) & v3_pre_topc(tptp_fun_B_21(A), A) & v4_pre_topc(tptp_fun_B_21(A), A) & v1_membered(tptp_fun_B_21(A)) & v2_membered(tptp_fun_B_21(A)) & v3_membered(tptp_fun_B_21(A)) & v4_membered(tptp_fun_B_21(A)) & v5_membered(tptp_fun_B_21(A)) & v2_tops_1(tptp_fun_B_21(A), A) & v3_tops_1(tptp_fun_B_21(A), A)) <=> (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A))))), (((~(v2_pre_topc(A) & l1_pre_topc(A))) | (m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(tptp_fun_B_21(A)) & v3_pre_topc(tptp_fun_B_21(A), A) & v4_pre_topc(tptp_fun_B_21(A), A) & v1_membered(tptp_fun_B_21(A)) & v2_membered(tptp_fun_B_21(A)) & v3_membered(tptp_fun_B_21(A)) & v4_membered(tptp_fun_B_21(A)) & v5_membered(tptp_fun_B_21(A)) & v2_tops_1(tptp_fun_B_21(A), A) & v3_tops_1(tptp_fun_B_21(A), A))) <=> (((~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A))))))), rewrite((((~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A))))) <=> ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A)))))), (((~(v2_pre_topc(A) & l1_pre_topc(A))) | (m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(tptp_fun_B_21(A)) & v3_pre_topc(tptp_fun_B_21(A), A) & v4_pre_topc(tptp_fun_B_21(A), A) & v1_membered(tptp_fun_B_21(A)) & v2_membered(tptp_fun_B_21(A)) & v3_membered(tptp_fun_B_21(A)) & v4_membered(tptp_fun_B_21(A)) & v5_membered(tptp_fun_B_21(A)) & v2_tops_1(tptp_fun_B_21(A), A) & v3_tops_1(tptp_fun_B_21(A), A))) <=> ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A)))))))),
% 5.01/5.18 inference(bind,[status(th)],[])).
% 5.01/5.18 tff(265,plain,
% 5.01/5.18 (![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | (m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(tptp_fun_B_21(A)) & v3_pre_topc(tptp_fun_B_21(A), A) & v4_pre_topc(tptp_fun_B_21(A), A) & v1_membered(tptp_fun_B_21(A)) & v2_membered(tptp_fun_B_21(A)) & v3_membered(tptp_fun_B_21(A)) & v4_membered(tptp_fun_B_21(A)) & v5_membered(tptp_fun_B_21(A)) & v2_tops_1(tptp_fun_B_21(A), A) & v3_tops_1(tptp_fun_B_21(A), A))) <=> ![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A)))))),
% 5.01/5.18 inference(quant_intro,[status(thm)],[264])).
% 5.01/5.18 tff(266,plain,
% 5.01/5.18 (![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A))) <=> ![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))),
% 5.01/5.18 inference(rewrite,[status(thm)],[])).
% 5.01/5.18 tff(267,plain,
% 5.01/5.18 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A))), ((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A))), ((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A)))), (((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A)) & v1_membered(B)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A)) & v1_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B))), (((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B)))), ((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B)) & v2_membered(B)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B)) & v2_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B))), ((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B)))), (((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B)) & v3_membered(B)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B)) & v3_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B))), (((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B)))), ((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B)) & v4_membered(B)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B)) & v4_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B))), ((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B)))), (((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B)) & v5_membered(B)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B)) & v5_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B))), (((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B)))), ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B)) & v2_tops_1(B, A)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B)) & v2_tops_1(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A))), ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A)))), (((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A)) <=> ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A)) & v3_tops_1(B, A)))), rewrite(((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A)) & v3_tops_1(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A))), (((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A)) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A))))), (?[B: $i] : ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A)) <=> ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))), (((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A))) <=> ((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A))))), rewrite(((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A))) <=> ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))), (((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A))) <=> ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))))),
% 5.01/5.18 inference(bind,[status(th)],[])).
% 5.01/5.18 tff(268,plain,
% 5.01/5.18 (![A: $i] : ((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A))) <=> ![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))),
% 5.01/5.18 inference(quant_intro,[status(thm)],[267])).
% 5.01/5.18 tff(269,axiom,(![A: $i] : ((v2_pre_topc(A) & l1_pre_topc(A)) => ?[B: $i] : ((((((((((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) & v3_pre_topc(B, A)) & v4_pre_topc(B, A)) & v1_membered(B)) & v2_membered(B)) & v3_membered(B)) & v4_membered(B)) & v5_membered(B)) & v2_tops_1(B, A)) & v3_tops_1(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc5_tops_1')).
% 5.01/5.18 tff(270,plain,
% 5.01/5.18 (![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[269, 268])).
% 5.01/5.18 tff(271,plain,
% 5.01/5.18 (![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | ?[B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B, A) & v4_pre_topc(B, A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B, A) & v3_tops_1(B, A)))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[270, 266])).
% 5.01/5.18 tff(272,plain,(
% 5.01/5.18 ![A: $i] : ((~(v2_pre_topc(A) & l1_pre_topc(A))) | (m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(tptp_fun_B_21(A)) & v3_pre_topc(tptp_fun_B_21(A), A) & v4_pre_topc(tptp_fun_B_21(A), A) & v1_membered(tptp_fun_B_21(A)) & v2_membered(tptp_fun_B_21(A)) & v3_membered(tptp_fun_B_21(A)) & v4_membered(tptp_fun_B_21(A)) & v5_membered(tptp_fun_B_21(A)) & v2_tops_1(tptp_fun_B_21(A), A) & v3_tops_1(tptp_fun_B_21(A), A)))),
% 5.01/5.18 inference(skolemize,[status(sab)],[271])).
% 5.01/5.18 tff(273,plain,
% 5.01/5.18 (![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A)))))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[272, 265])).
% 5.01/5.18 tff(274,plain,
% 5.01/5.18 (![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A)))))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[273, 263])).
% 5.01/5.18 tff(275,plain,
% 5.01/5.18 (((~![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A)))))) | ((~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~m1_subset_1(tptp_fun_B_21(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v3_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v1_membered(tptp_fun_B_21(A!0))) | (~v2_membered(tptp_fun_B_21(A!0))) | (~v3_membered(tptp_fun_B_21(A!0))) | (~v4_membered(tptp_fun_B_21(A!0))) | (~v5_membered(tptp_fun_B_21(A!0))) | (~v2_tops_1(tptp_fun_B_21(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_21(A!0), A!0)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A)))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~m1_subset_1(tptp_fun_B_21(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v3_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v1_membered(tptp_fun_B_21(A!0))) | (~v2_membered(tptp_fun_B_21(A!0))) | (~v3_membered(tptp_fun_B_21(A!0))) | (~v4_membered(tptp_fun_B_21(A!0))) | (~v5_membered(tptp_fun_B_21(A!0))) | (~v2_tops_1(tptp_fun_B_21(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_21(A!0), A!0)))))),
% 5.01/5.18 inference(rewrite,[status(thm)],[])).
% 5.01/5.18 tff(276,plain,
% 5.01/5.18 ((~![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A)))))) | ((~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~m1_subset_1(tptp_fun_B_21(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v3_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v1_membered(tptp_fun_B_21(A!0))) | (~v2_membered(tptp_fun_B_21(A!0))) | (~v3_membered(tptp_fun_B_21(A!0))) | (~v4_membered(tptp_fun_B_21(A!0))) | (~v5_membered(tptp_fun_B_21(A!0))) | (~v2_tops_1(tptp_fun_B_21(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_21(A!0), A!0)))))),
% 5.01/5.18 inference(quant_inst,[status(thm)],[])).
% 5.01/5.18 tff(277,plain,
% 5.01/5.18 ((~![A: $i] : ((~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~m1_subset_1(tptp_fun_B_21(A), k1_zfmisc_1(u1_struct_0(A)))) | (~v1_xboole_0(tptp_fun_B_21(A))) | (~v3_pre_topc(tptp_fun_B_21(A), A)) | (~v4_pre_topc(tptp_fun_B_21(A), A)) | (~v1_membered(tptp_fun_B_21(A))) | (~v2_membered(tptp_fun_B_21(A))) | (~v3_membered(tptp_fun_B_21(A))) | (~v4_membered(tptp_fun_B_21(A))) | (~v5_membered(tptp_fun_B_21(A))) | (~v2_tops_1(tptp_fun_B_21(A), A)) | (~v3_tops_1(tptp_fun_B_21(A), A)))))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~m1_subset_1(tptp_fun_B_21(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v3_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v1_membered(tptp_fun_B_21(A!0))) | (~v2_membered(tptp_fun_B_21(A!0))) | (~v3_membered(tptp_fun_B_21(A!0))) | (~v4_membered(tptp_fun_B_21(A!0))) | (~v5_membered(tptp_fun_B_21(A!0))) | (~v2_tops_1(tptp_fun_B_21(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_21(A!0), A!0))))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[276, 275])).
% 5.01/5.18 tff(278,plain,
% 5.01/5.18 (~((~m1_subset_1(tptp_fun_B_21(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v3_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v1_membered(tptp_fun_B_21(A!0))) | (~v2_membered(tptp_fun_B_21(A!0))) | (~v3_membered(tptp_fun_B_21(A!0))) | (~v4_membered(tptp_fun_B_21(A!0))) | (~v5_membered(tptp_fun_B_21(A!0))) | (~v2_tops_1(tptp_fun_B_21(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_21(A!0), A!0)))),
% 5.01/5.18 inference(unit_resolution,[status(thm)],[277, 87, 26, 274])).
% 5.01/5.18 tff(279,plain,
% 5.01/5.18 (((~m1_subset_1(tptp_fun_B_21(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v3_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v1_membered(tptp_fun_B_21(A!0))) | (~v2_membered(tptp_fun_B_21(A!0))) | (~v3_membered(tptp_fun_B_21(A!0))) | (~v4_membered(tptp_fun_B_21(A!0))) | (~v5_membered(tptp_fun_B_21(A!0))) | (~v2_tops_1(tptp_fun_B_21(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_21(A!0), A!0))) | v1_xboole_0(tptp_fun_B_21(A!0))),
% 5.01/5.18 inference(tautology,[status(thm)],[])).
% 5.01/5.18 tff(280,plain,
% 5.01/5.18 (v1_xboole_0(tptp_fun_B_21(A!0))),
% 5.01/5.18 inference(unit_resolution,[status(thm)],[279, 278])).
% 5.01/5.18 tff(281,plain,
% 5.01/5.18 (^[A: $i, B: $i] : refl(((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)) <=> ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))),
% 5.01/5.18 inference(bind,[status(th)],[])).
% 5.01/5.18 tff(282,plain,
% 5.01/5.18 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)) <=> ![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 5.01/5.18 inference(quant_intro,[status(thm)],[281])).
% 5.01/5.18 tff(283,plain,
% 5.01/5.18 (^[A: $i, B: $i] : trans(monotonicity(rewrite((v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)) <=> (~((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))), ((~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> (~(~((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))))), rewrite((~(~((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))) <=> ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))), ((~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))))),
% 5.01/5.18 inference(bind,[status(th)],[])).
% 5.01/5.18 tff(284,plain,
% 5.01/5.18 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 5.01/5.18 inference(quant_intro,[status(thm)],[283])).
% 5.01/5.18 tff(285,plain,
% 5.01/5.18 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 5.01/5.18 inference(rewrite,[status(thm)],[])).
% 5.01/5.18 tff(286,plain,
% 5.01/5.18 (^[A: $i, B: $i] : rewrite((~((v1_xboole_0(A) & (~(A = B))) & v1_xboole_0(B))) <=> (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))))),
% 5.01/5.18 inference(bind,[status(th)],[])).
% 5.01/5.18 tff(287,plain,
% 5.01/5.18 (![A: $i, B: $i] : (~((v1_xboole_0(A) & (~(A = B))) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 5.01/5.18 inference(quant_intro,[status(thm)],[286])).
% 5.01/5.18 tff(288,axiom,(![A: $i, B: $i] : (~((v1_xboole_0(A) & (~(A = B))) & v1_xboole_0(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 5.01/5.18 tff(289,plain,
% 5.01/5.18 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[288, 287])).
% 5.01/5.18 tff(290,plain,
% 5.01/5.18 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[289, 285])).
% 5.01/5.18 tff(291,plain,(
% 5.01/5.18 ![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 5.01/5.18 inference(skolemize,[status(sab)],[290])).
% 5.01/5.18 tff(292,plain,
% 5.01/5.18 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[291, 284])).
% 5.01/5.18 tff(293,plain,
% 5.01/5.18 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[292, 282])).
% 5.01/5.18 tff(294,plain,
% 5.01/5.18 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 5.01/5.18 inference(rewrite,[status(thm)],[])).
% 5.01/5.18 tff(295,axiom,(((((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)) & v4_membered(k1_xboole_0)) & v5_membered(k1_xboole_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_membered')).
% 5.01/5.18 tff(296,plain,
% 5.01/5.18 ((((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)) & v4_membered(k1_xboole_0)),
% 5.01/5.18 inference(and_elim,[status(thm)],[295])).
% 5.01/5.18 tff(297,plain,
% 5.01/5.18 (((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)),
% 5.01/5.18 inference(and_elim,[status(thm)],[296])).
% 5.01/5.18 tff(298,plain,
% 5.01/5.18 ((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)),
% 5.01/5.18 inference(and_elim,[status(thm)],[297])).
% 5.01/5.18 tff(299,plain,
% 5.01/5.18 (v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)),
% 5.01/5.18 inference(and_elim,[status(thm)],[298])).
% 5.01/5.18 tff(300,plain,
% 5.01/5.18 (v1_xboole_0(k1_xboole_0)),
% 5.01/5.18 inference(and_elim,[status(thm)],[299])).
% 5.01/5.18 tff(301,plain,
% 5.01/5.18 (v1_xboole_0(k1_xboole_0)),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[300, 294])).
% 5.01/5.18 tff(302,plain,
% 5.01/5.18 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (tptp_fun_B_21(A!0) = k1_xboole_0))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (tptp_fun_B_21(A!0) = k1_xboole_0))),
% 5.01/5.18 inference(rewrite,[status(thm)],[])).
% 5.01/5.18 tff(303,plain,
% 5.01/5.18 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (tptp_fun_B_21(A!0) = k1_xboole_0))),
% 5.01/5.18 inference(quant_inst,[status(thm)],[])).
% 5.01/5.18 tff(304,plain,
% 5.01/5.18 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (tptp_fun_B_21(A!0) = k1_xboole_0)),
% 5.01/5.18 inference(modus_ponens,[status(thm)],[303, 302])).
% 5.01/5.18 tff(305,plain,
% 5.01/5.18 (tptp_fun_B_21(A!0) = k1_xboole_0),
% 5.01/5.18 inference(unit_resolution,[status(thm)],[304, 301, 293, 280])).
% 5.01/5.18 tff(306,plain,
% 5.01/5.19 (((~m1_subset_1(tptp_fun_B_15(u1_struct_0(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0))))) | v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))),
% 5.01/5.19 inference(tautology,[status(thm)],[])).
% 5.01/5.19 tff(307,plain,
% 5.01/5.19 (v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))),
% 5.01/5.19 inference(unit_resolution,[status(thm)],[306, 229])).
% 5.01/5.19 tff(308,plain,
% 5.01/5.19 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))) | (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))) | (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0))))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(309,plain,
% 5.01/5.19 (((~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0)))) <=> ((~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))) | (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0))))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(310,plain,
% 5.01/5.19 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))) | (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0)))))),
% 5.01/5.19 inference(monotonicity,[status(thm)],[309])).
% 5.01/5.19 tff(311,plain,
% 5.01/5.19 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))) | (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0))))),
% 5.01/5.19 inference(transitivity,[status(thm)],[310, 308])).
% 5.01/5.19 tff(312,plain,
% 5.01/5.19 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0))))),
% 5.01/5.19 inference(quant_inst,[status(thm)],[])).
% 5.01/5.19 tff(313,plain,
% 5.01/5.19 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v1_xboole_0(tptp_fun_B_15(u1_struct_0(A!0)))) | (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0)))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[312, 311])).
% 5.01/5.19 tff(314,plain,
% 5.01/5.19 (tptp_fun_B_21(A!0) = tptp_fun_B_15(u1_struct_0(A!0))),
% 5.01/5.19 inference(unit_resolution,[status(thm)],[313, 293, 280, 307])).
% 5.01/5.19 tff(315,plain,
% 5.01/5.19 (tptp_fun_B_15(u1_struct_0(A!0)) = tptp_fun_B_21(A!0)),
% 5.01/5.19 inference(symmetry,[status(thm)],[314])).
% 5.01/5.19 tff(316,plain,
% 5.01/5.19 (tptp_fun_B_15(u1_struct_0(A!0)) = k1_xboole_0),
% 5.01/5.19 inference(transitivity,[status(thm)],[315, 305])).
% 5.01/5.19 tff(317,plain,
% 5.01/5.19 (k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3)),
% 5.01/5.19 inference(monotonicity,[status(thm)],[316])).
% 5.01/5.19 tff(318,plain,
% 5.01/5.19 (k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3) = k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3)),
% 5.01/5.19 inference(symmetry,[status(thm)],[317])).
% 5.01/5.19 tff(319,plain,
% 5.01/5.19 (m1_subset_1(tptp_fun_B_21(A!0), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.01/5.19 inference(monotonicity,[status(thm)],[305])).
% 5.01/5.19 tff(320,plain,
% 5.01/5.19 (((~m1_subset_1(tptp_fun_B_21(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(tptp_fun_B_21(A!0))) | (~v3_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v4_pre_topc(tptp_fun_B_21(A!0), A!0)) | (~v1_membered(tptp_fun_B_21(A!0))) | (~v2_membered(tptp_fun_B_21(A!0))) | (~v3_membered(tptp_fun_B_21(A!0))) | (~v4_membered(tptp_fun_B_21(A!0))) | (~v5_membered(tptp_fun_B_21(A!0))) | (~v2_tops_1(tptp_fun_B_21(A!0), A!0)) | (~v3_tops_1(tptp_fun_B_21(A!0), A!0))) | m1_subset_1(tptp_fun_B_21(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.01/5.19 inference(tautology,[status(thm)],[])).
% 5.01/5.19 tff(321,plain,
% 5.01/5.19 (m1_subset_1(tptp_fun_B_21(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.01/5.19 inference(unit_resolution,[status(thm)],[320, 278])).
% 5.01/5.19 tff(322,plain,
% 5.01/5.19 (m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[321, 319])).
% 5.01/5.19 tff(323,plain,
% 5.01/5.19 (^[A: $i, B: $i, C: $i] : refl(((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 5.01/5.19 inference(bind,[status(th)],[])).
% 5.01/5.19 tff(324,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.01/5.19 inference(quant_intro,[status(thm)],[323])).
% 5.01/5.19 tff(325,plain,
% 5.01/5.19 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B))) <=> ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B))) <=> ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 5.01/5.19 inference(bind,[status(th)],[])).
% 5.01/5.19 tff(326,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.01/5.19 inference(quant_intro,[status(thm)],[325])).
% 5.01/5.19 tff(327,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B)))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(328,plain,
% 5.01/5.19 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k4_subset_1(A, C, B))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B))))),
% 5.01/5.19 inference(bind,[status(th)],[])).
% 5.01/5.19 tff(329,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k4_subset_1(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B)))),
% 5.01/5.19 inference(quant_intro,[status(thm)],[328])).
% 5.01/5.19 tff(330,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k4_subset_1(A, C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k4_subset_1')).
% 5.01/5.19 tff(331,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B)))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[330, 329])).
% 5.01/5.19 tff(332,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B)))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[331, 327])).
% 5.01/5.19 tff(333,plain,(
% 5.01/5.19 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k4_subset_1(A, C, B)))),
% 5.01/5.19 inference(skolemize,[status(sab)],[332])).
% 5.01/5.19 tff(334,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[333, 326])).
% 5.01/5.19 tff(335,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[334, 324])).
% 5.01/5.19 tff(336,plain,
% 5.01/5.19 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3)))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3)))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(337,plain,
% 5.01/5.19 (((k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3)))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(338,plain,
% 5.01/5.19 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3))))),
% 5.01/5.19 inference(monotonicity,[status(thm)],[337])).
% 5.01/5.19 tff(339,plain,
% 5.01/5.19 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3)))),
% 5.01/5.19 inference(transitivity,[status(thm)],[338, 336])).
% 5.01/5.19 tff(340,plain,
% 5.01/5.19 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.01/5.19 inference(quant_inst,[status(thm)],[])).
% 5.01/5.19 tff(341,plain,
% 5.01/5.19 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[340, 339])).
% 5.01/5.19 tff(342,plain,
% 5.01/5.19 (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, D!3)),
% 5.01/5.19 inference(unit_resolution,[status(thm)],[341, 257, 335, 322])).
% 5.01/5.19 tff(343,plain,
% 5.01/5.19 (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3)),
% 5.01/5.19 inference(transitivity,[status(thm)],[342, 318])).
% 5.01/5.19 tff(344,plain,
% 5.01/5.19 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3))),
% 5.01/5.19 inference(monotonicity,[status(thm)],[343])).
% 5.01/5.19 tff(345,plain,
% 5.01/5.19 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))),
% 5.01/5.19 inference(transitivity,[status(thm)],[344, 261])).
% 5.01/5.19 tff(346,plain,
% 5.01/5.19 (m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.01/5.19 inference(monotonicity,[status(thm)],[345])).
% 5.01/5.19 tff(347,plain,
% 5.01/5.19 (^[A: $i, B: $i, C: $i] : refl((m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 5.01/5.19 inference(bind,[status(th)],[])).
% 5.01/5.19 tff(348,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.01/5.19 inference(quant_intro,[status(thm)],[347])).
% 5.01/5.19 tff(349,plain,
% 5.01/5.19 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 5.01/5.19 inference(bind,[status(th)],[])).
% 5.01/5.19 tff(350,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.01/5.19 inference(quant_intro,[status(thm)],[349])).
% 5.01/5.19 tff(351,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(352,plain,
% 5.01/5.19 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))))),
% 5.01/5.19 inference(bind,[status(th)],[])).
% 5.01/5.19 tff(353,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 5.01/5.19 inference(quant_intro,[status(thm)],[352])).
% 5.01/5.19 tff(354,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_subset_1')).
% 5.01/5.19 tff(355,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[354, 353])).
% 5.01/5.19 tff(356,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[355, 351])).
% 5.01/5.19 tff(357,plain,(
% 5.01/5.19 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 5.01/5.19 inference(skolemize,[status(sab)],[356])).
% 5.01/5.19 tff(358,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[357, 350])).
% 5.01/5.19 tff(359,plain,
% 5.01/5.19 (![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[358, 348])).
% 5.01/5.19 tff(360,plain,
% 5.01/5.19 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(361,plain,
% 5.01/5.19 ((m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(362,plain,
% 5.01/5.19 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.01/5.19 inference(monotonicity,[status(thm)],[361])).
% 5.01/5.19 tff(363,plain,
% 5.01/5.19 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.01/5.19 inference(transitivity,[status(thm)],[362, 360])).
% 5.01/5.19 tff(364,plain,
% 5.01/5.19 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.01/5.19 inference(quant_inst,[status(thm)],[])).
% 5.01/5.19 tff(365,plain,
% 5.01/5.19 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[364, 363])).
% 5.01/5.19 tff(366,plain,
% 5.01/5.19 (m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.01/5.19 inference(unit_resolution,[status(thm)],[365, 257, 359, 322])).
% 5.01/5.19 tff(367,plain,
% 5.01/5.19 (^[A: $i, B: $i] : refl((m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))) <=> (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))))),
% 5.01/5.19 inference(bind,[status(th)],[])).
% 5.01/5.19 tff(368,plain,
% 5.01/5.19 (![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 5.01/5.19 inference(quant_intro,[status(thm)],[367])).
% 5.01/5.19 tff(369,plain,
% 5.01/5.19 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))), (((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))))),
% 5.01/5.19 inference(bind,[status(th)],[])).
% 5.01/5.19 tff(370,plain,
% 5.01/5.19 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 5.01/5.19 inference(quant_intro,[status(thm)],[369])).
% 5.01/5.19 tff(371,plain,
% 5.01/5.19 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(372,plain,
% 5.01/5.19 (^[A: $i, B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), (((((~v3_struct_0(A)) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))), (((((~v3_struct_0(A)) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))))),
% 5.01/5.19 inference(bind,[status(th)],[])).
% 5.01/5.19 tff(373,plain,
% 5.01/5.19 (![A: $i, B: $i] : ((((~v3_struct_0(A)) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 5.01/5.19 inference(quant_intro,[status(thm)],[372])).
% 5.01/5.19 tff(374,axiom,(![A: $i, B: $i] : ((((~v3_struct_0(A)) & l1_pre_topc(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_tex_4')).
% 5.01/5.19 tff(375,plain,
% 5.01/5.19 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[374, 373])).
% 5.01/5.19 tff(376,plain,
% 5.01/5.19 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[375, 371])).
% 5.01/5.19 tff(377,plain,(
% 5.01/5.19 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))))),
% 5.01/5.19 inference(skolemize,[status(sab)],[376])).
% 5.01/5.19 tff(378,plain,
% 5.01/5.19 (![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[377, 370])).
% 5.01/5.19 tff(379,plain,
% 5.01/5.19 (![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 5.01/5.19 inference(modus_ponens,[status(thm)],[378, 368])).
% 5.01/5.19 tff(380,plain,
% 5.01/5.19 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(381,plain,
% 5.01/5.19 ((m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.01/5.19 inference(rewrite,[status(thm)],[])).
% 5.01/5.19 tff(382,plain,
% 5.01/5.19 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 5.01/5.19 inference(monotonicity,[status(thm)],[381])).
% 5.01/5.19 tff(383,plain,
% 5.01/5.19 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.03/5.19 inference(transitivity,[status(thm)],[382, 380])).
% 5.03/5.19 tff(384,plain,
% 5.03/5.19 ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))),
% 5.03/5.19 inference(quant_inst,[status(thm)],[])).
% 5.03/5.19 tff(385,plain,
% 5.03/5.19 ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.03/5.19 inference(modus_ponens,[status(thm)],[384, 383])).
% 5.03/5.19 tff(386,plain,
% 5.03/5.19 (m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.03/5.19 inference(unit_resolution,[status(thm)],[385, 88, 26, 379, 366])).
% 5.03/5.19 tff(387,plain,
% 5.03/5.19 (m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.03/5.19 inference(modus_ponens,[status(thm)],[386, 346])).
% 5.03/5.19 tff(388,plain,
% 5.03/5.19 (^[A: $i] : refl(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 5.03/5.19 inference(bind,[status(th)],[])).
% 5.03/5.19 tff(389,plain,
% 5.03/5.19 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 5.03/5.19 inference(quant_intro,[status(thm)],[388])).
% 5.03/5.19 tff(390,plain,
% 5.03/5.19 (^[A: $i] : rewrite(((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))),
% 5.03/5.19 inference(bind,[status(th)],[])).
% 5.03/5.19 tff(391,plain,
% 5.03/5.19 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 5.03/5.19 inference(quant_intro,[status(thm)],[390])).
% 5.03/5.19 tff(392,plain,
% 5.03/5.19 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 5.03/5.19 inference(transitivity,[status(thm)],[391, 389])).
% 5.03/5.19 tff(393,plain,
% 5.03/5.19 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 5.03/5.19 inference(rewrite,[status(thm)],[])).
% 5.03/5.19 tff(394,plain,
% 5.03/5.19 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), ((l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> (l1_pre_topc(A) => ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))))), rewrite((l1_pre_topc(A) => ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), ((l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))))),
% 5.03/5.19 inference(bind,[status(th)],[])).
% 5.03/5.19 tff(395,plain,
% 5.03/5.19 (![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 5.03/5.19 inference(quant_intro,[status(thm)],[394])).
% 5.03/5.19 tff(396,axiom,(![A: $i] : (l1_pre_topc(A) => ![B: $i] : (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_tsep_1')).
% 5.03/5.19 tff(397,plain,
% 5.03/5.19 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 5.03/5.19 inference(modus_ponens,[status(thm)],[396, 395])).
% 5.03/5.19 tff(398,plain,
% 5.03/5.19 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 5.03/5.19 inference(modus_ponens,[status(thm)],[397, 393])).
% 5.03/5.19 tff(399,plain,(
% 5.03/5.19 ![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 5.03/5.19 inference(skolemize,[status(sab)],[398])).
% 5.03/5.19 tff(400,plain,
% 5.03/5.19 (![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))),
% 5.03/5.19 inference(modus_ponens,[status(thm)],[399, 392])).
% 5.03/5.19 tff(401,plain,
% 5.03/5.19 (((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.03/5.19 inference(rewrite,[status(thm)],[])).
% 5.03/5.19 tff(402,plain,
% 5.03/5.19 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | ((~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.03/5.19 inference(quant_inst,[status(thm)],[])).
% 5.03/5.19 tff(403,plain,
% 5.03/5.19 ((~![A: $i] : ((~l1_pre_topc(A)) | ![B: $i] : ((~m1_pre_topc(B, A)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))))) | (~l1_pre_topc(A!0)) | ![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.03/5.19 inference(modus_ponens,[status(thm)],[402, 401])).
% 5.03/5.19 tff(404,plain,
% 5.03/5.19 (![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.03/5.19 inference(unit_resolution,[status(thm)],[403, 26, 400])).
% 5.03/5.19 tff(405,plain,
% 5.03/5.19 (((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | (~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.03/5.19 inference(rewrite,[status(thm)],[])).
% 5.03/5.19 tff(406,plain,
% 5.03/5.19 ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.03/5.19 inference(quant_inst,[status(thm)],[])).
% 5.03/5.19 tff(407,plain,
% 5.03/5.19 ((~![B: $i] : ((~m1_pre_topc(B, A!0)) | m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))) | (~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.03/5.19 inference(modus_ponens,[status(thm)],[406, 405])).
% 5.03/5.19 tff(408,plain,
% 5.03/5.19 ((~m1_pre_topc(B!1, A!0)) | m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.03/5.19 inference(unit_resolution,[status(thm)],[407, 404])).
% 5.03/5.19 tff(409,plain,
% 5.03/5.19 (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.03/5.19 inference(unit_resolution,[status(thm)],[408, 71])).
% 5.03/5.19 tff(410,plain,
% 5.03/5.19 (^[A: $i, B: $i, C: $i] : refl(((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 5.03/5.19 inference(bind,[status(th)],[])).
% 5.03/5.19 tff(411,plain,
% 5.03/5.19 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.03/5.19 inference(quant_intro,[status(thm)],[410])).
% 5.03/5.19 tff(412,plain,
% 5.03/5.19 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 5.03/5.19 inference(bind,[status(th)],[])).
% 5.03/5.19 tff(413,plain,
% 5.03/5.19 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.03/5.19 inference(quant_intro,[status(thm)],[412])).
% 5.03/5.19 tff(414,plain,
% 5.03/5.19 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 5.03/5.19 inference(rewrite,[status(thm)],[])).
% 5.03/5.19 tff(415,plain,
% 5.03/5.19 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C))))),
% 5.03/5.19 inference(bind,[status(th)],[])).
% 5.03/5.19 tff(416,plain,
% 5.03/5.19 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 5.03/5.20 inference(quant_intro,[status(thm)],[415])).
% 5.03/5.20 tff(417,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k5_subset_1')).
% 5.03/5.20 tff(418,plain,
% 5.03/5.20 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 5.03/5.20 inference(modus_ponens,[status(thm)],[417, 416])).
% 5.03/5.20 tff(419,plain,
% 5.03/5.20 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 5.03/5.20 inference(modus_ponens,[status(thm)],[418, 414])).
% 5.03/5.20 tff(420,plain,(
% 5.03/5.20 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k5_subset_1(A, B, C) = k3_xboole_0(B, C)))),
% 5.03/5.20 inference(skolemize,[status(sab)],[419])).
% 5.03/5.20 tff(421,plain,
% 5.03/5.20 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.03/5.20 inference(modus_ponens,[status(thm)],[420, 413])).
% 5.03/5.20 tff(422,plain,
% 5.03/5.20 (![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 5.03/5.20 inference(modus_ponens,[status(thm)],[421, 411])).
% 5.03/5.20 tff(423,plain,
% 5.03/5.20 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))))),
% 5.03/5.20 inference(rewrite,[status(thm)],[])).
% 5.03/5.20 tff(424,plain,
% 5.03/5.20 (((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))))),
% 5.03/5.20 inference(rewrite,[status(thm)],[])).
% 5.03/5.20 tff(425,plain,
% 5.03/5.20 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))))))),
% 5.03/5.20 inference(monotonicity,[status(thm)],[424])).
% 5.03/5.20 tff(426,plain,
% 5.03/5.20 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))))),
% 5.03/5.20 inference(transitivity,[status(thm)],[425, 423])).
% 5.03/5.20 tff(427,plain,
% 5.03/5.20 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.03/5.20 inference(quant_inst,[status(thm)],[])).
% 5.03/5.20 tff(428,plain,
% 5.03/5.20 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))))),
% 5.03/5.20 inference(modus_ponens,[status(thm)],[427, 426])).
% 5.03/5.20 tff(429,plain,
% 5.03/5.20 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))),
% 5.03/5.20 inference(unit_resolution,[status(thm)],[428, 422, 409, 387])).
% 5.03/5.20 tff(430,plain,
% 5.03/5.20 (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3))),
% 5.03/5.20 inference(symmetry,[status(thm)],[261])).
% 5.03/5.20 tff(431,plain,
% 5.03/5.20 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3)))),
% 5.03/5.20 inference(monotonicity,[status(thm)],[430])).
% 5.03/5.20 tff(432,plain,
% 5.03/5.20 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))),
% 5.03/5.20 inference(symmetry,[status(thm)],[431])).
% 5.03/5.20 tff(433,plain,
% 5.03/5.20 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3)) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))),
% 5.03/5.20 inference(symmetry,[status(thm)],[344])).
% 5.03/5.20 tff(434,plain,
% 5.03/5.20 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)))),
% 5.03/5.20 inference(monotonicity,[status(thm)],[433])).
% 5.03/5.20 tff(435,plain,
% 5.03/5.20 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), D!3)))),
% 5.03/5.20 inference(symmetry,[status(thm)],[434])).
% 5.03/5.20 tff(436,plain,
% 5.03/5.20 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))))))),
% 5.03/5.20 inference(bind,[status(th)],[])).
% 5.03/5.20 tff(437,plain,
% 5.03/5.20 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))),
% 5.03/5.20 inference(quant_intro,[status(thm)],[436])).
% 5.03/5.20 tff(438,plain,
% 5.03/5.20 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))))),
% 5.03/5.20 inference(bind,[status(th)],[])).
% 5.03/5.20 tff(439,plain,
% 5.03/5.20 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 5.03/5.20 inference(quant_intro,[status(thm)],[438])).
% 5.03/5.20 tff(440,plain,
% 5.03/5.20 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))))),
% 5.03/5.20 inference(bind,[status(th)],[])).
% 5.03/5.20 tff(441,plain,
% 5.03/5.20 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 5.03/5.20 inference(quant_intro,[status(thm)],[440])).
% 5.03/5.20 tff(442,plain,
% 5.03/5.20 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 5.03/5.20 inference(transitivity,[status(thm)],[441, 439])).
% 5.03/5.20 tff(443,plain,
% 5.03/5.20 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) <=> (~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))), ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) <=> (~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)))), ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), trans(monotonicity(rewrite((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) <=> (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))), trans(monotonicity(rewrite((m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))) <=> (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))), (((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) <=> ((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))), rewrite(((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))) <=> ((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))), (((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) <=> ((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))), (((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))) <=> ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))), rewrite(((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) <=> (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))), (((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))) <=> (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))), (![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))) <=> ((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))), rewrite(((v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))), (((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))) <=> (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))) <=> ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))))),
% 5.03/5.20 inference(bind,[status(th)],[])).
% 5.03/5.20 tff(444,plain,
% 5.03/5.20 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 5.03/5.20 inference(quant_intro,[status(thm)],[443])).
% 5.03/5.20 tff(445,plain,
% 5.03/5.20 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (((~(C = k4_tsp_2(A, B))) | ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 5.03/5.20 inference(bind,[status(th)],[])).
% 5.03/5.20 tff(446,plain,
% 5.03/5.20 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (((~(C = k4_tsp_2(A, B))) | ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))),
% 5.03/5.20 inference(quant_intro,[status(thm)],[445])).
% 5.03/5.20 tff(447,plain,
% 5.03/5.20 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))),
% 5.03/5.20 inference(rewrite,[status(thm)],[])).
% 5.03/5.20 tff(448,plain,
% 5.03/5.20 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) <=> ((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))) <=> ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))), (![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))) <=> (((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))), rewrite((((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))), (((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))) <=> ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))))), (![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))),
% 5.03/5.21 inference(bind,[status(th)],[])).
% 5.03/5.21 tff(449,plain,
% 5.03/5.21 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))),
% 5.03/5.21 inference(quant_intro,[status(thm)],[448])).
% 5.03/5.21 tff(450,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v2_tsp_2(B, A)) & m2_tsp_1(B, A)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v5_pre_topc(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((C = k4_tsp_2(A, B)) <=> ![D: $i] : (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) => ((D = u1_struct_0(B)) => ![E: $i] : (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) => (k5_subset_1(u1_struct_0(A), D, k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d12_tsp_2')).
% 5.03/5.21 tff(451,plain,
% 5.03/5.21 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))),
% 5.03/5.21 inference(modus_ponens,[status(thm)],[450, 449])).
% 5.03/5.21 tff(452,plain,
% 5.03/5.21 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((C = k4_tsp_2(A, B)) <=> ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))),
% 5.03/5.21 inference(modus_ponens,[status(thm)],[451, 447])).
% 5.03/5.21 tff(453,plain,(
% 5.03/5.21 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (((~(C = k4_tsp_2(A, B))) | ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))),
% 5.03/5.21 inference(skolemize,[status(sab)],[452])).
% 5.03/5.21 tff(454,plain,
% 5.03/5.21 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_tsp_2(B, A) & m2_tsp_1(B, A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ((![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B)))) & ((C = k4_tsp_2(A, B)) | (m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A))) & (~((~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A)))))))))))),
% 5.03/5.21 inference(modus_ponens,[status(thm)],[453, 446])).
% 5.03/5.21 tff(455,plain,
% 5.03/5.21 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 5.03/5.21 inference(modus_ponens,[status(thm)],[454, 444])).
% 5.03/5.21 tff(456,plain,
% 5.03/5.21 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))))) | (~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))))))))),
% 5.03/5.21 inference(modus_ponens,[status(thm)],[455, 442])).
% 5.03/5.21 tff(457,plain,
% 5.03/5.21 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))),
% 5.03/5.21 inference(modus_ponens,[status(thm)],[456, 437])).
% 5.03/5.21 tff(458,plain,
% 5.03/5.21 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))))))))),
% 5.03/5.21 inference(rewrite,[status(thm)],[])).
% 5.03/5.21 tff(459,plain,
% 5.03/5.21 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E)))))))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))))))))),
% 5.03/5.21 inference(rewrite,[status(thm)],[])).
% 5.03/5.21 tff(460,plain,
% 5.03/5.21 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))))),
% 5.03/5.21 inference(monotonicity,[status(thm)],[459])).
% 5.03/5.21 tff(461,plain,
% 5.03/5.21 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))))))))))),
% 5.05/5.21 inference(transitivity,[status(thm)],[460, 458])).
% 5.05/5.21 tff(462,plain,
% 5.05/5.21 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A!0)) | (~m2_tsp_1(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))))))))))),
% 5.05/5.21 inference(quant_inst,[status(thm)],[])).
% 5.05/5.21 tff(463,plain,
% 5.05/5.21 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | ![B: $i] : (v3_struct_0(B) | (~v2_tsp_2(B, A)) | (~m2_tsp_1(B, A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v5_pre_topc(C, A, B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A), k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, tptp_fun_E_4(C, B, A))) = k4_pre_topc(A, B, C, tptp_fun_E_4(C, B, A))))))) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) | (~(C = k4_tsp_2(A, B))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A)))) | (k5_subset_1(u1_struct_0(A), u1_struct_0(B), k3_tex_4(A, E)) = k4_pre_topc(A, B, C, E))))))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | ![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))),
% 5.05/5.21 inference(modus_ponens,[status(thm)],[462, 461])).
% 5.05/5.21 tff(464,plain,
% 5.05/5.21 (![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))),
% 5.05/5.21 inference(unit_resolution,[status(thm)],[463, 88, 87, 26, 457])).
% 5.05/5.21 tff(465,plain,
% 5.05/5.21 (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E)))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E)))))))))),
% 5.05/5.21 inference(rewrite,[status(thm)],[])).
% 5.05/5.21 tff(466,plain,
% 5.05/5.21 ((v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))) | (~(C = k4_tsp_2(A!0, B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))))))))) <=> (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E)))))))))),
% 5.05/5.21 inference(rewrite,[status(thm)],[])).
% 5.05/5.21 tff(467,plain,
% 5.05/5.21 (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))) | (~(C = k4_tsp_2(A!0, B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))))),
% 5.05/5.22 inference(monotonicity,[status(thm)],[466])).
% 5.05/5.22 tff(468,plain,
% 5.05/5.22 (((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))) | (~(C = k4_tsp_2(A!0, B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E)))))))))),
% 5.05/5.22 inference(transitivity,[status(thm)],[467, 465])).
% 5.05/5.22 tff(469,plain,
% 5.05/5.22 ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | (v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))) | (~(C = k4_tsp_2(A!0, B!1))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0))))))))))),
% 5.05/5.22 inference(quant_inst,[status(thm)],[])).
% 5.05/5.22 tff(470,plain,
% 5.05/5.22 ((~![B: $i] : (v3_struct_0(B) | (~m2_tsp_1(B, A!0)) | (~v2_tsp_2(B, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v5_pre_topc(C, A!0, B)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((C = k4_tsp_2(A!0, B)) | (~((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, tptp_fun_E_4(C, B, A!0))) = k4_pre_topc(A!0, B, C, tptp_fun_E_4(C, B, A!0))))))) | (~(![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B, C, E))) | (~(C = k4_tsp_2(A!0, B))) | (~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A!0))))))))))) | v3_struct_0(B!1) | (~m2_tsp_1(B!1, A!0)) | (~v2_tsp_2(B!1, A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))),
% 5.05/5.22 inference(modus_ponens,[status(thm)],[469, 468])).
% 5.05/5.22 tff(471,plain,
% 5.05/5.22 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))),
% 5.05/5.22 inference(unit_resolution,[status(thm)],[470, 86, 85, 31, 464])).
% 5.05/5.22 tff(472,plain,
% 5.05/5.22 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 5.05/5.22 inference(tautology,[status(thm)],[])).
% 5.05/5.22 tff(473,plain,
% 5.05/5.22 (v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)),
% 5.05/5.22 inference(unit_resolution,[status(thm)],[472, 159])).
% 5.05/5.22 tff(474,plain,
% 5.05/5.22 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 5.05/5.22 inference(tautology,[status(thm)],[])).
% 5.05/5.22 tff(475,plain,
% 5.05/5.22 (v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))),
% 5.05/5.22 inference(unit_resolution,[status(thm)],[474, 159])).
% 5.05/5.22 tff(476,plain,
% 5.05/5.22 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_1(k1_tsp_2(A!0, B!1))),
% 5.05/5.22 inference(tautology,[status(thm)],[])).
% 5.05/5.22 tff(477,plain,
% 5.05/5.22 (v1_funct_1(k1_tsp_2(A!0, B!1))),
% 5.05/5.22 inference(unit_resolution,[status(thm)],[476, 159])).
% 5.05/5.22 tff(478,plain,
% 5.05/5.22 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))),
% 5.05/5.22 inference(rewrite,[status(thm)],[])).
% 5.05/5.22 tff(479,plain,
% 5.05/5.22 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))))))) <=> ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))),
% 5.05/5.22 inference(rewrite,[status(thm)],[])).
% 5.05/5.22 tff(480,plain,
% 5.05/5.22 ((~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))))) <=> (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))))))),
% 5.05/5.22 inference(rewrite,[status(thm)],[])).
% 5.05/5.22 tff(481,plain,
% 5.05/5.22 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))))))) <=> ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))),
% 5.05/5.22 inference(monotonicity,[status(thm)],[480])).
% 5.05/5.22 tff(482,plain,
% 5.05/5.22 (((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))))))) <=> ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))),
% 5.05/5.22 inference(transitivity,[status(thm)],[481, 479])).
% 5.05/5.22 tff(483,plain,
% 5.05/5.22 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))))))))),
% 5.05/5.22 inference(monotonicity,[status(thm)],[482])).
% 5.05/5.22 tff(484,plain,
% 5.05/5.22 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))))),
% 5.05/5.23 inference(transitivity,[status(thm)],[483, 478])).
% 5.05/5.23 tff(485,plain,
% 5.05/5.23 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | ((~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))))))))),
% 5.05/5.23 inference(quant_inst,[status(thm)],[])).
% 5.05/5.23 tff(486,plain,
% 5.05/5.23 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(C, A!0, B!1)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((C = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(C, B!1, A!0))) = k4_pre_topc(A!0, B!1, C, tptp_fun_E_4(C, B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~(C = k4_tsp_2(A!0, B!1))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, C, E))))))))) | (~v1_funct_1(k1_tsp_2(A!0, B!1))) | (~v1_funct_2(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v5_pre_topc(k1_tsp_2(A!0, B!1), A!0, B!1)) | (~m2_relset_1(k1_tsp_2(A!0, B!1), u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))))))),
% 5.05/5.23 inference(modus_ponens,[status(thm)],[485, 484])).
% 5.05/5.23 tff(487,plain,
% 5.05/5.23 (~((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))))),
% 5.05/5.23 inference(unit_resolution,[status(thm)],[486, 477, 475, 473, 161, 471])).
% 5.05/5.23 tff(488,plain,
% 5.05/5.23 (((~((k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), tptp_fun_E_4(k1_tsp_2(A!0, B!1), B!1, A!0))))))) | (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))),
% 5.05/5.23 inference(tautology,[status(thm)],[])).
% 5.05/5.23 tff(489,plain,
% 5.05/5.23 ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))),
% 5.05/5.23 inference(unit_resolution,[status(thm)],[488, 487])).
% 5.05/5.23 tff(490,plain,
% 5.05/5.23 ((~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1)))),
% 5.05/5.23 inference(tautology,[status(thm)],[])).
% 5.05/5.23 tff(491,plain,
% 5.05/5.23 ((~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E))) | (~(k1_tsp_2(A!0, B!1) = k4_tsp_2(A!0, B!1))))) | ![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))),
% 5.05/5.23 inference(unit_resolution,[status(thm)],[490, 409, 125])).
% 5.05/5.23 tff(492,plain,
% 5.05/5.23 (![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))),
% 5.05/5.23 inference(unit_resolution,[status(thm)],[491, 489])).
% 5.05/5.23 tff(493,plain,
% 5.05/5.23 (((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | ((~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))))) <=> ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))))),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(494,plain,
% 5.05/5.23 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | ((~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))))),
% 5.05/5.23 inference(quant_inst,[status(thm)],[])).
% 5.05/5.23 tff(495,plain,
% 5.05/5.23 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)))),
% 5.05/5.23 inference(modus_ponens,[status(thm)],[494, 493])).
% 5.05/5.23 tff(496,plain,
% 5.05/5.23 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))),
% 5.05/5.23 inference(unit_resolution,[status(thm)],[495, 492, 366])).
% 5.05/5.23 tff(497,plain,
% 5.05/5.23 (k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)))),
% 5.05/5.23 inference(symmetry,[status(thm)],[496])).
% 5.05/5.23 tff(498,plain,
% 5.05/5.23 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0)))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0)))),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(499,plain,
% 5.05/5.23 (((k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0)))),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(500,plain,
% 5.05/5.23 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0))))),
% 5.05/5.23 inference(monotonicity,[status(thm)],[499])).
% 5.05/5.23 tff(501,plain,
% 5.05/5.23 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0)))),
% 5.05/5.23 inference(transitivity,[status(thm)],[500, 498])).
% 5.05/5.23 tff(502,plain,
% 5.05/5.23 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.23 inference(quant_inst,[status(thm)],[])).
% 5.05/5.23 tff(503,plain,
% 5.05/5.23 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0))),
% 5.05/5.23 inference(modus_ponens,[status(thm)],[502, 501])).
% 5.05/5.23 tff(504,plain,
% 5.05/5.23 (k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0) = k2_xboole_0(D!3, k1_xboole_0)),
% 5.05/5.23 inference(unit_resolution,[status(thm)],[503, 257, 211, 322])).
% 5.05/5.23 tff(505,plain,
% 5.05/5.23 (k2_xboole_0(D!3, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)),
% 5.05/5.23 inference(symmetry,[status(thm)],[504])).
% 5.05/5.23 tff(506,plain,
% 5.05/5.23 (^[A: $i] : refl((k2_xboole_0(A, k1_xboole_0) = A) <=> (k2_xboole_0(A, k1_xboole_0) = A))),
% 5.05/5.23 inference(bind,[status(th)],[])).
% 5.05/5.23 tff(507,plain,
% 5.05/5.23 (![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A) <=> ![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)),
% 5.05/5.23 inference(quant_intro,[status(thm)],[506])).
% 5.05/5.23 tff(508,plain,
% 5.05/5.23 (![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A) <=> ![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(509,axiom,(![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_boole')).
% 5.05/5.23 tff(510,plain,
% 5.05/5.23 (![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)),
% 5.05/5.23 inference(modus_ponens,[status(thm)],[509, 508])).
% 5.05/5.23 tff(511,plain,(
% 5.05/5.23 ![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)),
% 5.05/5.23 inference(skolemize,[status(sab)],[510])).
% 5.05/5.23 tff(512,plain,
% 5.05/5.23 (![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)),
% 5.05/5.23 inference(modus_ponens,[status(thm)],[511, 507])).
% 5.05/5.23 tff(513,plain,
% 5.05/5.23 ((~![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)) | (k2_xboole_0(D!3, k1_xboole_0) = D!3)),
% 5.05/5.23 inference(quant_inst,[status(thm)],[])).
% 5.05/5.23 tff(514,plain,
% 5.05/5.23 (k2_xboole_0(D!3, k1_xboole_0) = D!3),
% 5.05/5.23 inference(unit_resolution,[status(thm)],[513, 512])).
% 5.05/5.23 tff(515,plain,
% 5.05/5.23 (D!3 = k2_xboole_0(D!3, k1_xboole_0)),
% 5.05/5.23 inference(symmetry,[status(thm)],[514])).
% 5.05/5.23 tff(516,plain,
% 5.05/5.23 (D!3 = k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)),
% 5.05/5.23 inference(transitivity,[status(thm)],[515, 505])).
% 5.05/5.23 tff(517,plain,
% 5.05/5.23 (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))),
% 5.05/5.23 inference(monotonicity,[status(thm)],[124, 516])).
% 5.05/5.23 tff(518,plain,
% 5.05/5.23 (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))),
% 5.05/5.23 inference(transitivity,[status(thm)],[517, 497, 435, 432, 429])).
% 5.05/5.23 tff(519,plain,
% 5.05/5.23 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.23 inference(and_elim,[status(thm)],[25])).
% 5.05/5.23 tff(520,plain,
% 5.05/5.23 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))))),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(521,plain,
% 5.05/5.23 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))))),
% 5.05/5.23 inference(quant_inst,[status(thm)],[])).
% 5.05/5.23 tff(522,plain,
% 5.05/5.23 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))),
% 5.05/5.23 inference(modus_ponens,[status(thm)],[521, 520])).
% 5.05/5.23 tff(523,plain,
% 5.05/5.23 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))),
% 5.05/5.23 inference(unit_resolution,[status(thm)],[522, 519, 255])).
% 5.05/5.23 tff(524,plain,
% 5.05/5.23 (k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2)),
% 5.05/5.23 inference(monotonicity,[status(thm)],[316])).
% 5.05/5.23 tff(525,plain,
% 5.05/5.23 (k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2) = k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2)),
% 5.05/5.23 inference(symmetry,[status(thm)],[524])).
% 5.05/5.23 tff(526,plain,
% 5.05/5.23 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2)))),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(527,plain,
% 5.05/5.23 (((k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2)))),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(528,plain,
% 5.05/5.23 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2))))),
% 5.05/5.23 inference(monotonicity,[status(thm)],[527])).
% 5.05/5.23 tff(529,plain,
% 5.05/5.23 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2)))),
% 5.05/5.23 inference(transitivity,[status(thm)],[528, 526])).
% 5.05/5.23 tff(530,plain,
% 5.05/5.23 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.23 inference(quant_inst,[status(thm)],[])).
% 5.05/5.23 tff(531,plain,
% 5.05/5.23 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2))),
% 5.05/5.23 inference(modus_ponens,[status(thm)],[530, 529])).
% 5.05/5.23 tff(532,plain,
% 5.05/5.23 (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), k1_xboole_0, C!2)),
% 5.05/5.23 inference(unit_resolution,[status(thm)],[531, 519, 335, 322])).
% 5.05/5.23 tff(533,plain,
% 5.05/5.23 (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2)),
% 5.05/5.23 inference(transitivity,[status(thm)],[532, 525])).
% 5.05/5.23 tff(534,plain,
% 5.05/5.23 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2))),
% 5.05/5.23 inference(monotonicity,[status(thm)],[533])).
% 5.05/5.23 tff(535,plain,
% 5.05/5.23 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))),
% 5.05/5.23 inference(transitivity,[status(thm)],[534, 523])).
% 5.05/5.23 tff(536,plain,
% 5.05/5.23 (m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.23 inference(monotonicity,[status(thm)],[535])).
% 5.05/5.23 tff(537,plain,
% 5.05/5.23 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(538,plain,
% 5.05/5.23 ((m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(539,plain,
% 5.05/5.23 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.23 inference(monotonicity,[status(thm)],[538])).
% 5.05/5.23 tff(540,plain,
% 5.05/5.23 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.23 inference(transitivity,[status(thm)],[539, 537])).
% 5.05/5.23 tff(541,plain,
% 5.05/5.23 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.23 inference(quant_inst,[status(thm)],[])).
% 5.05/5.23 tff(542,plain,
% 5.05/5.23 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.23 inference(modus_ponens,[status(thm)],[541, 540])).
% 5.05/5.23 tff(543,plain,
% 5.05/5.23 (m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.23 inference(unit_resolution,[status(thm)],[542, 519, 359, 322])).
% 5.05/5.23 tff(544,plain,
% 5.05/5.23 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(545,plain,
% 5.05/5.23 ((m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.23 inference(rewrite,[status(thm)],[])).
% 5.05/5.23 tff(546,plain,
% 5.05/5.23 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 5.05/5.24 inference(monotonicity,[status(thm)],[545])).
% 5.05/5.24 tff(547,plain,
% 5.05/5.24 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.24 inference(transitivity,[status(thm)],[546, 544])).
% 5.05/5.24 tff(548,plain,
% 5.05/5.24 ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))),
% 5.05/5.24 inference(quant_inst,[status(thm)],[])).
% 5.05/5.24 tff(549,plain,
% 5.05/5.24 ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.24 inference(modus_ponens,[status(thm)],[548, 547])).
% 5.05/5.24 tff(550,plain,
% 5.05/5.24 (m1_subset_1(k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.24 inference(unit_resolution,[status(thm)],[549, 88, 26, 379, 543])).
% 5.05/5.24 tff(551,plain,
% 5.05/5.24 (m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.24 inference(modus_ponens,[status(thm)],[550, 536])).
% 5.05/5.24 tff(552,plain,
% 5.05/5.24 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))))),
% 5.05/5.24 inference(rewrite,[status(thm)],[])).
% 5.05/5.24 tff(553,plain,
% 5.05/5.24 (((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))))),
% 5.05/5.24 inference(rewrite,[status(thm)],[])).
% 5.05/5.24 tff(554,plain,
% 5.05/5.24 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))))))),
% 5.05/5.24 inference(monotonicity,[status(thm)],[553])).
% 5.05/5.24 tff(555,plain,
% 5.05/5.24 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))))),
% 5.05/5.24 inference(transitivity,[status(thm)],[554, 552])).
% 5.05/5.24 tff(556,plain,
% 5.05/5.24 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.24 inference(quant_inst,[status(thm)],[])).
% 5.05/5.24 tff(557,plain,
% 5.05/5.24 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))))),
% 5.05/5.24 inference(modus_ponens,[status(thm)],[556, 555])).
% 5.05/5.24 tff(558,plain,
% 5.05/5.24 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))),
% 5.05/5.24 inference(unit_resolution,[status(thm)],[557, 422, 409, 551])).
% 5.05/5.24 tff(559,plain,
% 5.05/5.24 (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2))),
% 5.05/5.24 inference(symmetry,[status(thm)],[523])).
% 5.05/5.24 tff(560,plain,
% 5.05/5.24 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2)))),
% 5.05/5.24 inference(monotonicity,[status(thm)],[559])).
% 5.05/5.24 tff(561,plain,
% 5.05/5.24 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))),
% 5.05/5.24 inference(symmetry,[status(thm)],[560])).
% 5.05/5.24 tff(562,plain,
% 5.05/5.24 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2)) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))),
% 5.05/5.24 inference(symmetry,[status(thm)],[534])).
% 5.05/5.24 tff(563,plain,
% 5.05/5.24 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)))),
% 5.05/5.24 inference(monotonicity,[status(thm)],[562])).
% 5.05/5.24 tff(564,plain,
% 5.05/5.24 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), tptp_fun_B_15(u1_struct_0(A!0)), C!2)))),
% 5.05/5.24 inference(symmetry,[status(thm)],[563])).
% 5.05/5.24 tff(565,plain,
% 5.05/5.24 (((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | ((~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))))) <=> ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))))),
% 5.05/5.24 inference(rewrite,[status(thm)],[])).
% 5.05/5.24 tff(566,plain,
% 5.05/5.24 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | ((~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))))),
% 5.05/5.24 inference(quant_inst,[status(thm)],[])).
% 5.05/5.24 tff(567,plain,
% 5.05/5.24 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)))),
% 5.05/5.24 inference(modus_ponens,[status(thm)],[566, 565])).
% 5.05/5.24 tff(568,plain,
% 5.05/5.24 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))),
% 5.05/5.24 inference(unit_resolution,[status(thm)],[567, 492, 543])).
% 5.05/5.24 tff(569,plain,
% 5.05/5.24 (k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)))),
% 5.05/5.24 inference(symmetry,[status(thm)],[568])).
% 5.05/5.24 tff(570,plain,
% 5.05/5.24 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0)))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0)))),
% 5.05/5.24 inference(rewrite,[status(thm)],[])).
% 5.05/5.24 tff(571,plain,
% 5.05/5.24 (((k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0)))),
% 5.05/5.24 inference(rewrite,[status(thm)],[])).
% 5.05/5.24 tff(572,plain,
% 5.05/5.24 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0))))),
% 5.05/5.24 inference(monotonicity,[status(thm)],[571])).
% 5.05/5.24 tff(573,plain,
% 5.05/5.24 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0)))),
% 5.05/5.24 inference(transitivity,[status(thm)],[572, 570])).
% 5.05/5.24 tff(574,plain,
% 5.05/5.24 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.24 inference(quant_inst,[status(thm)],[])).
% 5.05/5.24 tff(575,plain,
% 5.05/5.24 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0))),
% 5.05/5.24 inference(modus_ponens,[status(thm)],[574, 573])).
% 5.05/5.24 tff(576,plain,
% 5.05/5.24 (k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0) = k2_xboole_0(C!2, k1_xboole_0)),
% 5.05/5.24 inference(unit_resolution,[status(thm)],[575, 519, 211, 322])).
% 5.05/5.24 tff(577,plain,
% 5.05/5.24 (k2_xboole_0(C!2, k1_xboole_0) = k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)),
% 5.05/5.24 inference(symmetry,[status(thm)],[576])).
% 5.05/5.24 tff(578,plain,
% 5.05/5.24 ((~![A: $i] : (k2_xboole_0(A, k1_xboole_0) = A)) | (k2_xboole_0(C!2, k1_xboole_0) = C!2)),
% 5.05/5.24 inference(quant_inst,[status(thm)],[])).
% 5.05/5.24 tff(579,plain,
% 5.05/5.24 (k2_xboole_0(C!2, k1_xboole_0) = C!2),
% 5.05/5.24 inference(unit_resolution,[status(thm)],[578, 512])).
% 5.05/5.24 tff(580,plain,
% 5.05/5.24 (C!2 = k2_xboole_0(C!2, k1_xboole_0)),
% 5.05/5.24 inference(symmetry,[status(thm)],[579])).
% 5.05/5.24 tff(581,plain,
% 5.05/5.24 (C!2 = k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)),
% 5.05/5.24 inference(transitivity,[status(thm)],[580, 577])).
% 5.05/5.24 tff(582,plain,
% 5.05/5.24 (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))),
% 5.05/5.24 inference(monotonicity,[status(thm)],[124, 581])).
% 5.05/5.24 tff(583,plain,
% 5.05/5.24 (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)))),
% 5.05/5.24 inference(transitivity,[status(thm)],[582, 569, 564, 561, 558])).
% 5.05/5.24 tff(584,plain,
% 5.05/5.24 (k2_xboole_0(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)) = k2_xboole_0(k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))), k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))))),
% 5.05/5.24 inference(monotonicity,[status(thm)],[583, 518])).
% 5.05/5.24 tff(585,plain,
% 5.05/5.24 (k2_xboole_0(k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))), k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))) = k2_xboole_0(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))),
% 5.05/5.24 inference(symmetry,[status(thm)],[584])).
% 5.05/5.24 tff(586,plain,
% 5.05/5.24 (^[A: $i, B: $i, C: $i] : refl((k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C))) <=> (k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C))))),
% 5.05/5.24 inference(bind,[status(th)],[])).
% 5.05/5.24 tff(587,plain,
% 5.05/5.24 (![A: $i, B: $i, C: $i] : (k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C))) <=> ![A: $i, B: $i, C: $i] : (k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C)))),
% 5.05/5.24 inference(quant_intro,[status(thm)],[586])).
% 5.05/5.24 tff(588,plain,
% 5.05/5.24 (![A: $i, B: $i, C: $i] : (k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C))) <=> ![A: $i, B: $i, C: $i] : (k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C)))),
% 5.05/5.24 inference(rewrite,[status(thm)],[])).
% 5.05/5.24 tff(589,axiom,(![A: $i, B: $i, C: $i] : (k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_xboole_1')).
% 5.05/5.24 tff(590,plain,
% 5.05/5.24 (![A: $i, B: $i, C: $i] : (k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C)))),
% 5.05/5.24 inference(modus_ponens,[status(thm)],[589, 588])).
% 5.05/5.24 tff(591,plain,(
% 5.05/5.24 ![A: $i, B: $i, C: $i] : (k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C)))),
% 5.05/5.24 inference(skolemize,[status(sab)],[590])).
% 5.05/5.24 tff(592,plain,
% 5.05/5.24 (![A: $i, B: $i, C: $i] : (k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C)))),
% 5.05/5.24 inference(modus_ponens,[status(thm)],[591, 587])).
% 5.05/5.24 tff(593,plain,
% 5.05/5.24 ((~![A: $i, B: $i, C: $i] : (k3_xboole_0(A, k2_xboole_0(B, C)) = k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C)))) | (k3_xboole_0(u1_struct_0(B!1), k2_xboole_0(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))) = k2_xboole_0(k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))), k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))))),
% 5.05/5.24 inference(quant_inst,[status(thm)],[])).
% 5.05/5.24 tff(594,plain,
% 5.05/5.24 (k3_xboole_0(u1_struct_0(B!1), k2_xboole_0(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))) = k2_xboole_0(k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2))), k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))))),
% 5.05/5.24 inference(unit_resolution,[status(thm)],[593, 592])).
% 5.05/5.24 tff(595,plain,
% 5.05/5.24 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C)))))),
% 5.05/5.24 inference(rewrite,[status(thm)],[])).
% 5.05/5.24 tff(596,plain,
% 5.05/5.24 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C)))))),
% 5.05/5.24 inference(quant_inst,[status(thm)],[])).
% 5.05/5.24 tff(597,plain,
% 5.05/5.24 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C))))),
% 5.05/5.24 inference(modus_ponens,[status(thm)],[596, 595])).
% 5.05/5.24 tff(598,plain,
% 5.05/5.24 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C))))),
% 5.05/5.24 inference(unit_resolution,[status(thm)],[597, 257, 251])).
% 5.05/5.24 tff(599,plain,
% 5.05/5.24 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C!2)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C!2)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))))),
% 5.05/5.24 inference(rewrite,[status(thm)],[])).
% 5.05/5.24 tff(600,plain,
% 5.05/5.24 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C!2)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))))),
% 5.05/5.24 inference(quant_inst,[status(thm)],[])).
% 5.05/5.24 tff(601,plain,
% 5.05/5.24 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C!2)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))),
% 5.05/5.24 inference(modus_ponens,[status(thm)],[600, 599])).
% 5.05/5.24 tff(602,plain,
% 5.05/5.24 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C!2)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))),
% 5.05/5.24 inference(unit_resolution,[status(thm)],[601, 519, 598])).
% 5.05/5.24 tff(603,plain,
% 5.05/5.24 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2)))),
% 5.05/5.24 inference(rewrite,[status(thm)],[])).
% 5.05/5.24 tff(604,plain,
% 5.05/5.24 (((k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2)))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(605,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2))))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[604])).
% 5.05/5.25 tff(606,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2)))),
% 5.05/5.25 inference(transitivity,[status(thm)],[605, 603])).
% 5.05/5.25 tff(607,plain,
% 5.05/5.25 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.25 inference(quant_inst,[status(thm)],[])).
% 5.05/5.25 tff(608,plain,
% 5.05/5.25 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k4_subset_1(A, C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2))),
% 5.05/5.25 inference(modus_ponens,[status(thm)],[607, 606])).
% 5.05/5.25 tff(609,plain,
% 5.05/5.25 (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2)),
% 5.05/5.25 inference(unit_resolution,[status(thm)],[608, 519, 257, 335])).
% 5.05/5.25 tff(610,plain,
% 5.05/5.25 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C!2))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[609])).
% 5.05/5.25 tff(611,plain,
% 5.05/5.25 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, C)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, C)))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(612,plain,
% 5.05/5.25 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, C)))))),
% 5.05/5.25 inference(quant_inst,[status(thm)],[])).
% 5.05/5.25 tff(613,plain,
% 5.05/5.25 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), B, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, B), k3_tex_4(A!0, C)))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, C))))),
% 5.05/5.25 inference(modus_ponens,[status(thm)],[612, 611])).
% 5.05/5.25 tff(614,plain,
% 5.05/5.25 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, C))))),
% 5.05/5.25 inference(unit_resolution,[status(thm)],[613, 519, 251])).
% 5.05/5.25 tff(615,plain,
% 5.05/5.25 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, C))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, C))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(616,plain,
% 5.05/5.25 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, C))))) | ((~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))))),
% 5.05/5.25 inference(quant_inst,[status(thm)],[])).
% 5.05/5.25 tff(617,plain,
% 5.05/5.25 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, C)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, C))))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)))),
% 5.05/5.25 inference(modus_ponens,[status(thm)],[616, 615])).
% 5.05/5.25 tff(618,plain,
% 5.05/5.25 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))),
% 5.05/5.25 inference(unit_resolution,[status(thm)],[617, 257, 614])).
% 5.05/5.25 tff(619,plain,
% 5.05/5.25 (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, D!3))),
% 5.05/5.25 inference(symmetry,[status(thm)],[618])).
% 5.05/5.25 tff(620,plain,
% 5.05/5.25 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(621,plain,
% 5.05/5.25 ((m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(622,plain,
% 5.05/5.25 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[621])).
% 5.05/5.25 tff(623,plain,
% 5.05/5.25 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.25 inference(transitivity,[status(thm)],[622, 620])).
% 5.05/5.25 tff(624,plain,
% 5.05/5.25 ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))),
% 5.05/5.25 inference(quant_inst,[status(thm)],[])).
% 5.05/5.25 tff(625,plain,
% 5.05/5.25 ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.25 inference(modus_ponens,[status(thm)],[624, 623])).
% 5.05/5.25 tff(626,plain,
% 5.05/5.25 (m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.25 inference(unit_resolution,[status(thm)],[625, 88, 26, 257, 379])).
% 5.05/5.25 tff(627,plain,
% 5.05/5.25 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(628,plain,
% 5.05/5.25 ((m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(629,plain,
% 5.05/5.25 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[628])).
% 5.05/5.25 tff(630,plain,
% 5.05/5.25 (((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.25 inference(transitivity,[status(thm)],[629, 627])).
% 5.05/5.25 tff(631,plain,
% 5.05/5.25 ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))),
% 5.05/5.25 inference(quant_inst,[status(thm)],[])).
% 5.05/5.25 tff(632,plain,
% 5.05/5.25 ((~![A: $i, B: $i] : (m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A))) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)) | m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.25 inference(modus_ponens,[status(thm)],[631, 630])).
% 5.05/5.25 tff(633,plain,
% 5.05/5.25 (m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.25 inference(unit_resolution,[status(thm)],[632, 88, 26, 519, 379])).
% 5.05/5.25 tff(634,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(635,plain,
% 5.05/5.25 (((k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(636,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)))))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[635])).
% 5.05/5.25 tff(637,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))))),
% 5.05/5.25 inference(transitivity,[status(thm)],[636, 634])).
% 5.05/5.25 tff(638,plain,
% 5.05/5.25 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.25 inference(quant_inst,[status(thm)],[])).
% 5.05/5.25 tff(639,plain,
% 5.05/5.25 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)))),
% 5.05/5.25 inference(modus_ponens,[status(thm)],[638, 637])).
% 5.05/5.25 tff(640,plain,
% 5.05/5.25 ((~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)))),
% 5.05/5.25 inference(unit_resolution,[status(thm)],[639, 211])).
% 5.05/5.25 tff(641,plain,
% 5.05/5.25 (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))),
% 5.05/5.25 inference(unit_resolution,[status(thm)],[640, 633, 626])).
% 5.05/5.25 tff(642,plain,
% 5.05/5.25 (k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3)) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))),
% 5.05/5.25 inference(symmetry,[status(thm)],[641])).
% 5.05/5.25 tff(643,plain,
% 5.05/5.25 (k3_tex_4(A!0, D!3) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[516])).
% 5.05/5.25 tff(644,plain,
% 5.05/5.25 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, k1_xboole_0)) = k3_tex_4(A!0, D!3)),
% 5.05/5.25 inference(symmetry,[status(thm)],[643])).
% 5.05/5.25 tff(645,plain,
% 5.05/5.25 (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)) = k3_tex_4(A!0, D!3)),
% 5.05/5.25 inference(transitivity,[status(thm)],[430, 433, 644])).
% 5.05/5.25 tff(646,plain,
% 5.05/5.25 (k3_tex_4(A!0, C!2) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[581])).
% 5.05/5.25 tff(647,plain,
% 5.05/5.25 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), C!2, k1_xboole_0)) = k3_tex_4(A!0, C!2)),
% 5.05/5.25 inference(symmetry,[status(thm)],[646])).
% 5.05/5.25 tff(648,plain,
% 5.05/5.25 (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)) = k3_tex_4(A!0, C!2)),
% 5.05/5.25 inference(transitivity,[status(thm)],[559, 562, 647])).
% 5.05/5.25 tff(649,plain,
% 5.05/5.25 (k2_xboole_0(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k2_xboole_0(k3_tex_4(A!0, C!2), k3_tex_4(A!0, D!3))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[648, 645])).
% 5.05/5.25 tff(650,plain,
% 5.05/5.25 (k2_xboole_0(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))) = k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))),
% 5.05/5.25 inference(transitivity,[status(thm)],[649, 642, 619, 610, 602])).
% 5.05/5.25 tff(651,plain,
% 5.05/5.25 (k3_xboole_0(u1_struct_0(B!1), k2_xboole_0(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3)))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[650])).
% 5.05/5.25 tff(652,plain,
% 5.05/5.25 (k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k2_xboole_0(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, C!2)), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, tptp_fun_B_15(u1_struct_0(A!0))), k3_tex_4(A!0, D!3))))),
% 5.05/5.25 inference(symmetry,[status(thm)],[651])).
% 5.05/5.25 tff(653,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(654,plain,
% 5.05/5.25 ((m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(655,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[654])).
% 5.05/5.25 tff(656,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.25 inference(transitivity,[status(thm)],[655, 653])).
% 5.05/5.25 tff(657,plain,
% 5.05/5.25 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.25 inference(quant_inst,[status(thm)],[])).
% 5.05/5.25 tff(658,plain,
% 5.05/5.25 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.25 inference(modus_ponens,[status(thm)],[657, 656])).
% 5.05/5.25 tff(659,plain,
% 5.05/5.25 ((~m1_subset_1(k3_tex_4(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k3_tex_4(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.25 inference(unit_resolution,[status(thm)],[658, 359])).
% 5.05/5.25 tff(660,plain,
% 5.05/5.25 (m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.25 inference(unit_resolution,[status(thm)],[659, 633, 626])).
% 5.05/5.25 tff(661,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(662,plain,
% 5.05/5.25 (((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))))),
% 5.05/5.25 inference(rewrite,[status(thm)],[])).
% 5.05/5.25 tff(663,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))))))),
% 5.05/5.25 inference(monotonicity,[status(thm)],[662])).
% 5.05/5.25 tff(664,plain,
% 5.05/5.25 (((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))))),
% 5.05/5.25 inference(transitivity,[status(thm)],[663, 661])).
% 5.05/5.25 tff(665,plain,
% 5.05/5.25 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.25 inference(quant_inst,[status(thm)],[])).
% 5.05/5.25 tff(666,plain,
% 5.05/5.25 ((~![A: $i, B: $i, C: $i] : ((k5_subset_1(A, B, C) = k3_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))))),
% 5.05/5.25 inference(modus_ponens,[status(thm)],[665, 664])).
% 5.05/5.25 tff(667,plain,
% 5.05/5.25 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k3_xboole_0(u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))),
% 5.05/5.26 inference(unit_resolution,[status(thm)],[666, 422, 409, 660])).
% 5.05/5.26 tff(668,plain,
% 5.05/5.26 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3)))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3)))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(669,plain,
% 5.05/5.26 (((k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3)))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(670,plain,
% 5.05/5.26 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3))))),
% 5.05/5.26 inference(monotonicity,[status(thm)],[669])).
% 5.05/5.26 tff(671,plain,
% 5.05/5.26 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3)))),
% 5.05/5.26 inference(transitivity,[status(thm)],[670, 668])).
% 5.05/5.26 tff(672,plain,
% 5.05/5.26 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.26 inference(quant_inst,[status(thm)],[])).
% 5.05/5.26 tff(673,plain,
% 5.05/5.26 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[672, 671])).
% 5.05/5.26 tff(674,plain,
% 5.05/5.26 (k4_subset_1(u1_struct_0(A!0), C!2, D!3) = k2_xboole_0(C!2, D!3)),
% 5.05/5.26 inference(unit_resolution,[status(thm)],[673, 519, 257, 211])).
% 5.05/5.26 tff(675,plain,
% 5.05/5.26 (k2_xboole_0(C!2, D!3) = k4_subset_1(u1_struct_0(A!0), C!2, D!3)),
% 5.05/5.26 inference(symmetry,[status(thm)],[674])).
% 5.05/5.26 tff(676,plain,
% 5.05/5.26 (k2_xboole_0(C!2, D!3) = k4_subset_1(u1_struct_0(A!0), D!3, C!2)),
% 5.05/5.26 inference(transitivity,[status(thm)],[675, 609])).
% 5.05/5.26 tff(677,plain,
% 5.05/5.26 (k3_tex_4(A!0, k2_xboole_0(C!2, D!3)) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C!2))),
% 5.05/5.26 inference(monotonicity,[status(thm)],[676])).
% 5.05/5.26 tff(678,plain,
% 5.05/5.26 (k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C!2)) = k3_tex_4(A!0, k2_xboole_0(C!2, D!3))),
% 5.05/5.26 inference(symmetry,[status(thm)],[677])).
% 5.05/5.26 tff(679,plain,
% 5.05/5.26 (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)) = k3_tex_4(A!0, k4_subset_1(u1_struct_0(A!0), D!3, C!2))),
% 5.05/5.26 inference(symmetry,[status(thm)],[602])).
% 5.05/5.26 tff(680,plain,
% 5.05/5.26 (k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)) = k3_tex_4(A!0, k2_xboole_0(C!2, D!3))),
% 5.05/5.26 inference(transitivity,[status(thm)],[679, 678])).
% 5.05/5.26 tff(681,plain,
% 5.05/5.26 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k2_xboole_0(C!2, D!3)))),
% 5.05/5.26 inference(monotonicity,[status(thm)],[680])).
% 5.05/5.26 tff(682,plain,
% 5.05/5.26 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k2_xboole_0(C!2, D!3))) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k4_subset_1(u1_struct_0(A!0), k3_tex_4(A!0, D!3), k3_tex_4(A!0, C!2)))),
% 5.05/5.26 inference(symmetry,[status(thm)],[681])).
% 5.05/5.26 tff(683,plain,
% 5.05/5.26 (m1_subset_1(k2_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.26 inference(monotonicity,[status(thm)],[675])).
% 5.05/5.26 tff(684,plain,
% 5.05/5.26 (m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k2_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.26 inference(symmetry,[status(thm)],[683])).
% 5.05/5.26 tff(685,plain,
% 5.05/5.26 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(686,plain,
% 5.05/5.26 ((m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(687,plain,
% 5.05/5.26 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.26 inference(monotonicity,[status(thm)],[686])).
% 5.05/5.26 tff(688,plain,
% 5.05/5.26 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0))))),
% 5.05/5.26 inference(transitivity,[status(thm)],[687, 685])).
% 5.05/5.26 tff(689,plain,
% 5.05/5.26 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 5.05/5.26 inference(quant_inst,[status(thm)],[])).
% 5.05/5.26 tff(690,plain,
% 5.05/5.26 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[689, 688])).
% 5.05/5.26 tff(691,plain,
% 5.05/5.26 (m1_subset_1(k4_subset_1(u1_struct_0(A!0), C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.26 inference(unit_resolution,[status(thm)],[690, 519, 257, 359])).
% 5.05/5.26 tff(692,plain,
% 5.05/5.26 (m1_subset_1(k2_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0)))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[691, 684])).
% 5.05/5.26 tff(693,plain,
% 5.05/5.26 (((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | ((~m1_subset_1(k2_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k2_xboole_0(C!2, D!3))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k2_xboole_0(C!2, D!3))))) <=> ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | (~m1_subset_1(k2_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k2_xboole_0(C!2, D!3))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k2_xboole_0(C!2, D!3))))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(694,plain,
% 5.05/5.26 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | ((~m1_subset_1(k2_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k2_xboole_0(C!2, D!3))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k2_xboole_0(C!2, D!3))))),
% 5.05/5.26 inference(quant_inst,[status(thm)],[])).
% 5.05/5.26 tff(695,plain,
% 5.05/5.26 ((~![E: $i] : ((~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, E)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), E)))) | (~m1_subset_1(k2_xboole_0(C!2, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k2_xboole_0(C!2, D!3))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k2_xboole_0(C!2, D!3)))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[694, 693])).
% 5.05/5.26 tff(696,plain,
% 5.05/5.26 (k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k2_xboole_0(C!2, D!3))) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k2_xboole_0(C!2, D!3))),
% 5.05/5.26 inference(unit_resolution,[status(thm)],[695, 692, 492])).
% 5.05/5.26 tff(697,plain,
% 5.05/5.26 (k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k2_xboole_0(C!2, D!3)) = k5_subset_1(u1_struct_0(A!0), u1_struct_0(B!1), k3_tex_4(A!0, k2_xboole_0(C!2, D!3)))),
% 5.05/5.26 inference(symmetry,[status(thm)],[696])).
% 5.05/5.26 tff(698,plain,
% 5.05/5.26 (k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k2_xboole_0(C!2, D!3)) = k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3))),
% 5.05/5.26 inference(monotonicity,[status(thm)],[125, 675])).
% 5.05/5.26 tff(699,plain,
% 5.05/5.26 (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_pre_topc(A!0, B!1, k1_tsp_2(A!0, B!1), k2_xboole_0(C!2, D!3))),
% 5.05/5.28 inference(symmetry,[status(thm)],[698])).
% 5.05/5.28 tff(700,plain,
% 5.05/5.28 (k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3))),
% 5.05/5.28 inference(transitivity,[status(thm)],[699, 697, 682, 667, 652, 594, 585, 217])).
% 5.05/5.28 tff(701,plain,
% 5.05/5.28 (~(k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), k4_subset_1(u1_struct_0(A!0), C!2, D!3)) = k4_subset_1(u1_struct_0(B!1), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), C!2), k4_pre_topc(A!0, B!1, k4_tsp_2(A!0, B!1), D!3)))),
% 5.05/5.28 inference(or_elim,[status(thm)],[256])).
% 5.05/5.28 tff(702,plain,
% 5.05/5.28 ($false),
% 5.05/5.28 inference(unit_resolution,[status(thm)],[701, 700])).
% 5.05/5.28 % SZS output end Proof
% 5.05/5.29 % E exiting
%------------------------------------------------------------------------------